Tottenham manager Tim Sherwood believes the race for a top-four Premier League finish will "go down to the wire".
Spurs went above Everton into fifth place in the table with a 1-0 win at White Hart Lane on Sunday and are now only three points behind Liverpool, who occupy the final Champions League spot.
"We are happy we are amongst it and leap-frogged Everton, and now we're chasing Liverpool," said Sherwood.
"I've said it's going to the wire, today was huge, it was a cup final."
Tottenham, who qualified for the Champions League in 2010 and 2012, overcame Everton thanks to a clinical strike from Emmanuel Adebayor, who had their sole effort on target.
"You won't win games three or four nil all the time," said Sherwood after seeing his sixth victory from nine league games in charge.
"We had to dig in there today. If you want to get where we want to be you'll have to sometimes win without playing well."
Sherwood, 45, singled out Adebayor and goalkeeper Hugo Lloris - who made a couple of smart stops - for praise.
This was only Everton's fourth defeat in the Premier League, and they remain five points behind fourth-placed Liverpool.
Roberto Martinez described the result as "harsh", especially given their impressive first-half display at White Hart Lane.
"This type of performance in the next 13 games will get us a lot of points," said Martinez.
"We are fighting with ourselves. Thirteen games is a lot of points and the league is developing into one of most exciting ends to a season ever.
"It's down to us now to reproduce this level of performance but get the result [as well]."
Like Sherwood, the Spaniard expects the battle for a top-four finish to run until the end of the season.
Martinez added: "Today is a blow but it depends how we take it. It could be a real turning point.
"I think we were the better side. It comes down to concentration levels and know-how, and we need to make sure we take [lessons] from this defeat."
Everton, who have responded from their previous three league defeats with victories, host Crystal Palace at Goodison Park on Wednesday.
Tottenham, meanwhile, face a trip to Newcastle.