The Upton Park outfit travel to face Diame's new club – Hull City – on Monday as they look for their second Premier League win of the season.
Diame left West Ham on transfer deadline day and last week claimed he was being "shunted around" under Allardyce and that his regular use in different positions was "not good for my career".
Allardyce responded on Friday, though, and revealed that a drop in performances was behind his switch from central midfield.
"It's Mo's opinion, isn't it? He had two seasons with us," Allardyce said.
"We expected him to improve on his first season and he did not go on as far as we expected from there on.
"Mo would have continued to play in centre midfield had his performances continued to be as good as his first season.
"Those performances didn't quite live up to the ones he gave us in his early part of his career here with us.
"My responsibility is the team and the whole team, not one player. I have to look after 25 players and select the best team. If he wasn't happy and he's moved on then that's fine.
"A player picks himself. A player drops himself - not me. When the performances don't fall to the level you expect then the position is in jeopardy."
Diame's departure allowed Allardyce to bring in France midfielder Morgan Amalfitano from Marseille on an undisclosed fee.
And Allardyce is excited by the potential of the 29-year-old, who spent last term on loan at West Brom.
"Mo Diame leaving allowed us to get Morgan in," he added.
"He was coming to the end of his contract and Hull made us a good offer. It was good business all around as it allowed us to get Morgan in, and Mo got what he wanted as well.
"His overall play at West Brom and Marseille was what interested me in him.
"He's a creator with a few goals to add to that. Goals were a struggle for us last season, not the performances, and he can play a number of positions."
On reports a deadline day move for Manchester City's Micah Richards fell through, Allardyce said: "That's not strictly true. We could not meet the financial demands of Man City."
