"When Mark took over as manager of Peterborough United they were in a relegation battle and in the relegation zone," said Bevan.
"It is very disappointing for a club to part with a manager after only 13 games in charge when there are still 18 league games to play this season.
"I am sure that a manager of Mark's potential will be back in management in the not too distant future."
Cooper was appointed as Posh boss after two seasons at Blue Square Premier side Kettering Town.
But, ahead of Saturday's 2-0 defeat at Crystal Palace, he was forced to play down rumours of unrest among his squad.
The club have confirmed director of football Barry Fry will not be taking over the managerial role.
Captain George Boyd told BBC Radio Cambridgeshire: "Everyone knows Mark Cooper is a lovely bloke, the boys got on really well with him. In terms of man management he was very good."
Referring to reported unrest in the London Road squad Boyd added: "There was no problem in the first place. If anything this will bring us closer together.
"I don't know where it has come from, we just want to get Peterborough out this position."
Midfielder Paul Coutts has been linked with rejoining former boss Ferguson at Preston North End, while striker Aaron Mclean has been transfer listed at his own request.
Chairman Darragh MacAnthony heaped pressure on the management and players last week with a statement on the club's official website.
He said: "I have to apologise to all Posh fans for this season up until now.
"It's been nothing short of a disaster. I can understand their frustrations.
"I am done with defending the players, the previous management, current management and everyone else at the football club top to bottom."
Cooper leaves with his team 11 points adrift of safety in the Championship.
After starting with a defeat at Sheffield united, Posh lost just two of Cooper's next seven league games in charge, at Coventry City and West Bromwich Albion.
And, of the four draws they enjoyed, as well as a 2-1 win over Watford, one of them was an heroic effort at home to promotion-chasing Cardiff City, when they came from four goals down at half-time to draw 4-4.
But, since then, starting with a 4-0 FA Cup third round thumping at Tottenham, they have lost their last five games.
Posh are yet to announce who will be in charge for Saturday's home game with Queens Park Rangers.
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