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Everton goalkeeper Jordan Pickford told BBC Sport: "We know we weren't great in the first half and we didn't do what we were expected to, but if you don't play well and it's still 0-0 it's a great stepping stone. The lads came out flying after the break and it was great to get momentum with the early goal."
On his own performance: "I have just got to knuckle down and train better and play better and show people what I can do. It's football, and you can play good one week and maybe not the other, but it's about being mentally strong and that's one of the best aspects of my game.
"Last week didn't work out but we bounced back. We have to perform for the fans to get them going and that happened today. We aim to win every game we play and it doesn't matter who it's against. We want to finish the season strong."
Maurizio Sarri speaking to BBC Sport: "We played the first half really, really well. We could have scored in five or six different situations. We stopped playing. We didn't defend. It is incredible.
"After a first half that was so good, the level of motivation was very high and the level of application was very high then suddenly we stopped. It is very difficult to explain.
"I am not concerned [by lack of ruthlessness] because in the first half we created a lot of opportunities. Then, sooner or later you are able to score. I am worried about the second half!
"Of course today was important for us so now we have less opportunities. We have to fight and defend our opportunities."Copyright: Getty Images
Chelsea defender Antonio Rudiger told Sky Sports: "It was the same against Wolves, but this time we lost. We played a good first half but we didn't score. It is unacceptable the way we came out [after the break] and we lost the game in 10 minutes.
"We were passive and that is dangerous in this league. We played well in the first half, but the way we approached the second half was unacceptable."
On the mood in the changing room: "Everyone deals with it differently but it's unacceptable and I'm sorry. We still have eight games to go but we cannot always say 'next week,' we really have to do better because we normally aren't allowed to lose this match."
Few more thoughts from Maurizio Sarri and Antonio Rudiger on Chelsea's collapse in the second half...
More from Everton boss Marco Silva to BBC Sport: "Jordan Pickford deserved a very, very good performance.
"He achieved so many important things last season - he became England's number one, he's playing for a big club and all the highlights are on him.
"So it's normal now to ask about him when good things happen and the same when not. He's a professional and open to us working with him on things and I'm sure he will achieve what he deserves."
Everton boss Marco Silva, speaking to BBC Sport: "I said we have to do everything different to the first half. They tried but not in the way we planned. We played forward, tried to create chances and that is our model.
"Everything I don't want and the second half was everything the way I want to play. I could see a desire to win the game and we could challenge a team like Chelsea. I'm very proud of the players because of what they did in the second half."
More from Marco Silva speaking to Match of the Day now...
ChelseaCopyright: Getty Images
Chelsea manager Maurizio Sarri told Sky Sports: "I don't know and the players don't know what happened in the second half. I cannot explain it. We played the best first half in the season and we could have scored four or five and then suddenly we stopped playing. It's very strange and we stopped to defend and counter attack.
"We were in control of the match and we played very well so we needed continue but we didn't defend at the start of the second half. We changed the system but it was the same.
"The problem was mental on the pitch, so the system and the tactics are not important. It wasn't about motivation because we started very well. We have to play eight matches now and we have to fight for our possibilities."
More from Everton boss Marco Silva: "It was fantastic performance from Jordan Pickford. He had some very, very good moments and helped us to win the match. Not just because of Jordan we lost the last game though.
"I don't have doubts about what i'm doing I'm the first one that wants more, needs more consistency, be more mature to achieve everything we want we deserve and what our fans deserve also. The fans were the key again because they were behind us then.
BBC Sport at Goodison Park
It was a resurgent second-half performance from Everton, who earned their first win against a established top six side since January 2017.
It was an afternoon when the talent at Marco Silva's disposal finally clicked and Goodison Park was back to its deafening best, with Ross Barkley cast as the pantomime villain.
Everton boss Marco Silva, speaking to Sky Sports: "It would be easier for me just to speak about the second half. The first half I didn't like it at all, we were not there from the first minute.
"What we did in the second half was everything we planned during the week. I didn't like the first half and told our players at half time that they have to do everything different.
"And they did. They showed great attitude, character and personality second half but we have to do it from the first minute.
"Desire is a strong word. We weren't without desire. They work really hard every day, I can't say anything about their attitude. But maybe we weren't focused on our role. What I saw in the second half is what we do every day in training."
"We didn't play in the second half. I cannot understand." Poor Maurizio Sarri has no answers for Chelsea's performance.
Here comes Maurizio Sarri... The first question is "the game turned on its head at the start of the second half. What happened?"
"Oh, I don't know!" he responds.
Well, that clears things up.
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Marco Silva has just been talking to the press. He's understandably very pleased with the result but does admit there was much more needed from their first half performance.
Full quotes to come shortly.Copyright: Reuters
Still no word from any of the Chelsea players or manager. Maurizio Sarri having a good go at them in the changing rooms?
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Nick UTA: Chelsea have gone full-Spurs.Copyright: Getty Images
Everton defender Seamus Coleman told Sky Sports: "Everything about the result is so important. We are very disappointed with the result against Newcastle but we had a great atmosphere here against Liverpool and the fans continued that today. We were lucky to be level at half time and we couldn't work them out but Richarlison scored and we got over the line.
"We obviously need to give them something to cheer about and that hasn't happened enough this year but we have got back into it over the last few games. We are capable of results like that but it's about being consistent and this is the challenge for us because we want to compete with the top six."
Everton goalscorer Gylfi Sigurdsson told Sky Sports: "We started on the front foot in the second half and it was completely different to the first period. We were poor before the break but we defended well in the first half and we stayed in the game. We always thought we would create chances and we took them after the break.
"There was more movement and we won a lot more second balls which was important. It is better to score form open play than penalties but I managed to put it away after he made the save. I thought were were defensively very good after taking the lead and it was nice to keep a clean sheet."