He has revealed he would have signed a new contract at Rovers - if he had been offered one earlier in the season.
Mowbray told Lancashire Live: "Undoubtedly, definitely. It's a club going the right way with a lot of good, young players.
"With total respect to the executives at the football club, I felt they were just waiting to see what was going to happen.
"Can we get in the play-offs, can we not? I felt as if if we don't, does that makes me a bad manager? I'm not good enough so I don't get a new contract? If we do get in, I'm a good manager and I get a contract.
"That's not how to do it. You have to like the person, you have to believe in the person and trust them to lead your club or you don't. The fact nothing was done, the answer was right in front of me. That's why the decision has been made and I wish them well and move on.
"The away support has been brilliant for this team, they deserve a good team. They deserve a team where they can go away and they can sing and have a good day."
Other names linked with the role in the early stages of Graeme Lee’s departure from the club include former Sunderland coach - now Rochdale boss – Robbie Stockdale and Halifax boss Pete Wild.
Pools’ search for a new boss is underway, though an appointment is not understood to be imminent.
There is strong interest in the job, especially given Pools’ strong cup success this season and comfortably securing their status in League Two following their return to the Football League.
Pools ended their campaign on Saturday with a home defeat to Colchester United, the players now on their summer break ahead of the return to pre-season training in June.