However, the duo made it clear that they want Allardyce to introduce a more exciting brand of of football at Upton Park next season.
"I think you know what you're getting with Big Sam," McAvennie told the club's official website. "I would like personally to see a bit more quality in the team - a few players who can get the ball down.
"If you put on a team on the park that excites the fans, then they will be behind you. The fans like seeing a bit of flair, but they won't see it go back to the old days because football is different."
West Ham finished last season in 13th place in the Premier League table.