Allardyce arrived at Goodison Park in November 2017 and managed just six months in charge on Merseyside before his sacking in May 2018.
“I hope people could see what I tried to put in during my time at Everton and what Sam [Allardyce] tried to put in because whatever people say about us, we did improve from 16th to 8th," Lee, who was Allardyce's No2 at Everton, told Radio City Talk.
When asked if supporters' criticism of Allardyce wasunfair, Lee continued: “I know it's unfair. But I can't speak for them.
"Sam does get a bad rep and I don't know why, I really don't, because he came into a difficult situation. You only have to look at the facts, it was a side that was struggling.
“In the very short space of time we were there, Sam's effect on the team, whatever you think about it, the style of play and that, got them from 16th to 8th and I think that was a vast improvement.
“I think if he was given more time to bring people in to the football club that he wanted, whether it be players or the staff, then I think he would have proved to be an even greater success."