In David Moyes' last home match in charge, the Goodison Park outfit were rampant and won thanks to a double from Belgian Kevin Mirallas.

Everton striker Victor Anichebe also had a host of chances to score, while Leon Osman also went close on several occasions.

Allardyce said his only player to emerge from the match with any credit was goalkeeper Jussi Jaaskelainen, with the veteran Finnish stopper making a string of terrific saves to prevent embarrassment for his team.

"The way we played today, I have to say, we were lucky to get away with a 2-0 (defeat)," Allardyce said.

"There was only one player who has been outstanding for us today, and that was Jussi Jaaskelainen, who made some absolutely outstanding saves."

Allardyce said his players struggled to cope with the atmosphere and emotion around the game, and he praised Everton's work off the ball throughout the contest.

"I warned the players before the game what it was going to be like and it was exactly that. We simply couldn't cope with it today," he said.

"I think it is always difficult coming here. But this occasion makes it even more difficult. We saw that not just with the performance of Everton players with the ball, it was the performance of the Everton players when they didn't have the ball. 

"They gave us no time on the ball whatsoever. As soon as they lost it, they ran us down, they shut us down, they squeezed us and pressed us, and we couldn't get anything going because of the energy they showed not just in possession, but also out of possession."