David Moyes enjoyed a perfect Goodison Park send-off as his Everton side beat West Ham 2-0 thanks to a double from Kevin Mirallas.
Speaking after the game, Moyes paid tribute to the Everton fans for their support.
"The crowd showed today what a big club Everton is, and I think today that was their part in it all. It was an emotional time during the second half because they got right behind their football club. They got the team that second goal."
Allardyce felt his team were lucky not to be embarrassed and claimed his goalkeeper was the only West Ham player to impress.
The way we played today we were lucky to get away with 2-0," he told Sky Sports. "There was only one player who has been outstanding for us and that was Jussi Jaaskelainen who made some outstanding saves."