Bryan Oviedo scored the only goal of the game to give the Blues a famous win, and the Spaniard insists that the scoreline was a fair reflection of the match.
"It was a big battle today. We were outstanding at playing Manchester United eye-to-eye," he told BBC Sport. "It is fair to say we did expect United to have their chances, but we were very confident with Tim Howard and our defenders.
"As an away team, you normally feel you will have only one or two chances maximum. But with our ambition, we created many, many chances. If you look at the overall position we deserved all three points and that is an incredible statement."
Everton lie in fifth place in the Premier League table following the result, while United slip down to ninth.