United took the lead through Dimitar Berbatov, but Everton fought back and won the game.
“It was a brilliant performance by the players because it’s never easy to beat Manchester United,” he told Sky Sports.
“We keep getting reminded how many times we have not beaten the top four, but Chelsea recently and now Man Utd have been here and we have beaten them both.”
He added: “I thought we didn’t start great, I thought Manchester United were better in the opening period, but I think we grew into the game.
“We started to get a bit of control in midfield and started to pass it around better and I thought in the second half we had one or two opportunities. And when we got them in the second half we took them.”
Youngsters Dan Gosling and Jack Rodwell scored two of the goals for Everton.
“People know they have come on in other big games and made a difference,” said the Scot.
“They are both talented with great potential to go on with age and experience, a bit like Wayne (Rooney) at times. We are trying to put them on the right path and they both came on and made an impact today.”