The Senegalese midfielder's existing contract ran out today.
Clark says the decision to let him go was made purely for financial reasons, rather than footballing ones.
Despite making just two first team appearances since joining the club in mid-October, Diop has been an extremely popular character with his teammates and around the club.
He has recently been suffering with a hamstring problem, but is close to returning to full fitness.
"We are not keeping him on because of the situation the club finds itself in," said the Blues boss. "He is a talented footballer who still has got a lot to offer, but unfortunately we cannot keep pursuing that deal.
"Of course I would have wanted to keep him. Forget my relationship with him and playing alongside him because that’s never come into the equation. What’s been the important thing is that he’s a good player and a fantastic character. He's also been a brilliant example to the young players of how to be a top player, how you stay there, how you train and how you prepare.
Clark continued: "It was one of the hardest meetings I’ve ever had to do, to tell a fellow like that. I don’t know why I’m surprised, but he took it like he is, which is man mountain and he accepted it. He just asked if he would be allowed to stay and use our facilities and train with us. I hope he does get another club and is ready to step into the breach."