Laudrup's tenure as manager of the Welsh outfit was ended on Tuesday, after a run of just one victory in 10 Premier League fixtures that left the club in 12th and just two points above the relegation zone.
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A statement from Jenkins on the club's official website read: "Everyone needs to move on; get behind us and focus on Saturday's game.
"The fact is, Michael's time with us has come to an end. But I have found some of the things being said about him today hard to stomach.
"Much of it has been extremely unsavoury and unnecessary. Too many people have been trying to play the blame game and unearth disrespectful reasons behind his departure.
"We were quite open and honest in our official statement, because that's the way we are as a club.
"Since then we have tried to keep our own counsel on the matter because we have nothing bad to say about Michael.
"He deserves respect for what he has done in the game and you couldn't meet a more genuine and honest person. It's time to move on."
Laudrup moved to the Liberty Stadium in June 2012 and won the Capital One Cup in his first season at the club, qualifying for the Europa League as a result.
Garry Monk has been placed in temporary charge, with his first game coming at home to fierce rivals Cardiff City on Saturday.