Goals from Steven Naismith, Romelu Lukaku and an own goal from Mikel Arteta moved the Toffes within one point of Arsene Wenger's faltering fourth-placed side, with a game in hand still to come.
"It was one of our signature performances since I've been here at Everton," he told Sky Sports. "They've [the Everton fans] waited all season for a blockbuster performance like this. They've gotten a few but this was definitely the one.
"We have to believe [Everton can get top four] because we're running out of games, so we'd like to think we can."
Meanwhile, Naismith says a top-four finish "would mean everything" to the club, but insisted himself and the rest of the squad must keep their feet on the ground with six games still to play.
"It [top four] would mean everything," Naismith said.
But we've believed from the start of the season and it just shows in these performances so we just need to concentrate going into next week and take the points."