The Toffees started their Premier League campaign with an away victory against Jose Mourinho’s men thanks to Dominic Calvert-Lewin’s lone goal at the Tottenham Hotspur Stadium.
This was Everton’s first away win in 40 attempts against the traditional top six sides in the English top flight.
Ancelotti revealed he expected a cagey encounter but was left impressed with Everton’s performance.
"It was good, the game was what I expected from the team. It was not easy but we had energy, quality,” the former Chelsea and AC Milan manager told Sky Sports after the game.
“This performance gives us more confidence for the future. We showed what we can do. For the players it was important to show what they can do.”
“The performance was brilliant. We had difficulties at the beginning but we were comfortable on the pitch.”
Summer signings Abdoulaye Doucoure, Allan and James Rodriguez were handed their respective debuts, and the trio showed glimpses of what to expect from them this season against Spurs.
Ancelotti insisted that players of their caliber do not need time to adapt to their new surroundings.
The Italian coach added: “The players that can play football, they don't need a lot of time to adapt. James knows what he has to do, Allan and Doucoure the same.”
“I just said show your quality and they did. We had a good combination in midfield. Last season we had players with quality on the ball but you also have to play without the ball."