Assistant boss Steve Round felt Everton fully deserved their place in the FA Cup fifth round after seeing off Fulham.
The Merseysiders came from behind to win 2-1 at Goodison Park with headers from Denis Stracqualursi and Marouane Fellaini after a controversial Danny Murphy penalty.
John Heitinga was penalised in the 13th minute when the ball struck his arm as he attempted to block a Damien Duff shot but Everton otherwise dictated the game.
Round said: "I think we deserved it. Their goal was against the run of play. It was a very difficult decision for the referee to give and I don't envy him in those positions.
"It did hit his hand but I think it was more ball to hand than hand to ball.
"We didn't think it was a penalty, it was quite harsh, but to come back, the team showed great spirit, great togetherness.
"We got the goal and then I thought we would go on and win it. We showed more ambition and I thought every time we put the ball in the net from a shot or cross we looked a real threat."