The popular Italian was sacked this morning.
Cottee is relieved Zola's future has been resolved now rather than rumbling on over the summer.
He told Sky Sports News: "I am pleased they haven't messed around and it dragged on for months.
"If they are going to do it, get it done, but the fans will judge it on the calibre of the manager coming in. I think Gianfranco has done a decent job in difficult circumstances.
"It hasn't been easy for him, everything that could have gone wrong at West Ham has gone wrong.
"And at the end of the season Gianfranco and the players have done well to stay up.
"But having said that the results haven't been good enough and obviously the board have now made a decision."
Cottee added: "What I would criticise them (the board) for is not sacking him when they first arrived at the club.
"It did appear right from the start that Zola was not their man.
"Various things have happened through the season that have undermined the management and the players, emails and things getting into the press. That doesn't make for a happy camp. I don't think the board handled it very well."