Allardyce said: "I think he should have retired and given us all a chance. He's a pain in the neck.
"For me, he has always set the standard of what to try and achieve.
"He's built an empire, a huge force at Old Trafford at what was a down-and-out club when he took over.
"It had failed to achieve the levels of success it was supposed to for years.
"He has restructured the club from the bottom to the very top.
"He's not quite as calm as he used to be. He has not lost the passion, the determination and the drive and you see how quickly he's turned round a very, very difficult situation.
"It's just a few weeks ago that he was in the noose and everyone was calling for his head.
"He knows that is the expectation Manchester United brings, he knows the size of the club because he has made it that way.
"And I don't think his desire to go on has waned in any shape or form."