The Toffees kept their hopes of making it to Europe alive after delivering a hammer blow on the Hammers’ top four aspirations.
After a bright start to the game by David Moyes’ men, it was the visitors who broke the deadlock on the 24th minute mark when striker Dominic Calvert-Lewin latched onto Ben Godfrey's through ball to steer his low shot past Lukasz Fabianski.
Speaking to the media after the game, Ancelotti lauded his team’s spirit against the East Londoners.
"The spirit was good, attitude good,” the former Chelsea head coach said.
"We defended really well, it was not easy. But we covered the spaces in-between well and tried to play on the counter attack.
"In the second half we could do better but it doesn't matter. All the times when we have won away it is this this kind of performance, and with this we have won 11 away games, this is a lot.
"We knew it was a vital game because if we lost we are out [of European contention] no doubt because West Ham would go up, so it was vital and we are still in the fight.
"I'm not concerned about the possession West Ham had because possession doesn’t mean you score goals.
"We are not a possession team because we have different qualities. The correlation between possession and victory is not for football, it is for a another sport.
"We knew that this was a vital game and there is another on Thursday against Villa and we have to be ready.
"The attitude is the base of this team, with the attitude we are dead."
