Ronny Deila believes that Celtic have shown they can "bounce back" from setbacks after a sure footed display knocked Hearts out of the League Cup.
The holders progressed with a merited 2-1 victory at Tynecastle and have now won twice since losing to Molde in the Europa League last week.
"We controlled the game very well," manager Deila told BBC Scotland.
"We played three games in six days and I'm so proud of the boys, it was very strong to go out and get a result."
Hearts were difficult opponents to overcome in the first-half, setting up with a sound defensive approach.
But Celtic were able to rely on the striking expertise and creative instincts of Leigh Griffiths who scored a wonderful solo goal and created the second for Tom Rogic.
Deila also had to overcome injuries sustained in the pre-match warm-up by captain Scott Brown and the substitute Gary MacKay-Steven, with the former's place in the starting line-up taken by James Forrest.
"We play a lot of games and Gary was feeling a bit in his groin and we don't take any chances with that," Deila explained. "Broony was feeling something in his knee and we have to see in the picture tomorrow what that is."
The match was largely untidy until Griffiths weaved his way past several defenders in maroon to open the scoring on 71 minutes.
"Tom Rogic was very good when he came on, to produce some life into the game and we got some chances," added Deila. "Griffiths is always sniffing around and you can't give him an opportunity because he will score.
"It was a good performance by Leigh. He scores in almost every game. He loves scoring goals, he's a good football player and he works hard for the team. I'm very pleased that we have him.
"We deserved to win, they didn't have one goal chance before they scored. We were balanced, when we attacked they were wanting to hurt on us on the counter but that they didn't do that until we were 2-0 up.
"We're in the semi-final and we'll enjoy that, but it's a big game on Saturday [against nearest Premiership challengers Aberdeen] it could put us in a good situation in the league. I'm looking forward to what's coming up.
"We need to perform, we need to be ready. I like [that] the team has shown unbelievable determination, they've shown they can bounce back. I'm happy, we'll keep on going."
Hearts scored a late consolation when Arnaud Djoum scored from a corner kick with only a minute left to play, but Robbie Neilson thinks that his side's performance showed how far they have progressed.
Hearts lost to Celtic in both cup competitions last season, conceding seven goals and scoring none, but the Hearts head coach believes his team is stronger and more competitive now, even if he felt his players should have defended more robustly against Griffiths for the opening goal.
"I thought, first half, we kept our shape, worked hard and our game plan worked," Neilson said.
"In the second half we looked as though we could score a goal but they get the first goal when the boy bundles through three tackles that we should clear and he got a good finish, the second goal then makes it difficult.
"But we've come a long way in 18 months, we're still building and this was disappointing but it shows how far we've come.
[Djoum] is a player who can drive forward with the ball and he was fresh. Morgaro [Gomis] and Prince [Buaben] did great for us screening the back four but in the last 10 or 15 minutes we needed energy driving forward and he's going to be a big player for us.
"If [the goal] had come five minutes earlier it would have been different but I was pleased with our performance. Last year we got beaten 4-0 [in the Scottish League Cup] and this was only 2-1, we were good in the game and could have won it. Celtic were scrambling at the end, desperate to win."