He left Parkhead six months before his Celtic deal was due to expire after talks over an extension broke down.
He has now suggested Mowbray was happy to concede to his wage demands but was vetoed by chief executive Peter Lawwell and majority shareholder Dermot Desmond.
While not specifically denying there had been a difference of opinion over Caldwell, Mowbray said: "First and foremost, it should be said I've got a very strong relationship - working relationship - with the executives at the club and my chief executive, Peter, and with the major shareholder, Dermot.
"There's no animosity and nothing going on behind the scenes that anybody should try to read into."
Mowbray, who also denied Caldwell's claim that the Celtic boss had expressed a desire for him to stay, added: "I admire Gary Caldwell as a guy and as a football player.
"Yet, there was a negotiation that went on and on and never came to a conclusion to the point that he was running out of contract, a club made a bid and we accepted that bid.
"I don't think we need look too deeply into those comments.
"Certain mischievous avenues could try to create a wedge that is not there.
"I wish Gary all the very, very best. He's an excellent footballer, he's a wonderful individual and a good man.
"But it's wrong to say that there's a conflict of interest at this club with myself and my board."