Cole told The Sun: "It was a sad moment. Carlo got on with everyone and was a great man to be around.
"He was funny but he could be serious when need be and all the players will miss him.
"He's left his mark on Chelsea by winning the Double in his first year but we've got to move on now. It would be good to have a manager long term but that's down to the big boss upstairs Mr Abramovich and if he feels the need to change then he's going to do it. It's his club so it's up to him. He's the main man.
"When he comes into the dressing room I sit back a bit in awe of him because I have a lot of respect for the way he's built the club."