Bellew failed to make the 12st 7lb limit at the weigh-in, with Aleksy Kuziemski eventually stepping but who Cleverly beat comfortably.
Bellew is now eyeing a second chance to take on the Welsh champion.
"It was the darkest 36 hours of my life," he said. "I lost a stone in 24 hours and I just needed to lose a bit more. I just couldn't get it down any more and I was devastated.
"But that is just how it goes. What doesn't kill you makes you stronger. I have always been very strong mentally and I know how to rebound and get on with things.
"I'll just keep doing what I'm doing, setting my goals and striving to achieve them.
"My chance will come, without a shadow of a doubt. I think the exposure and the build-up between myself and Cleverly now is massive.
"People want to see the fight, everybody is itching to do it, so it is there."
Tony Bellew is scheduled to fight Ovill McKenzie defend his Commonwealth strap at the Liverpool Echo Arena on July 16.
The pair last met in December McKenzie floored the unbeaten Bellew twice in the early rounds before the champion earned an eighth round stoppage.
Speaking about that particular fight, Bellew said; "I went in there and started too slow - I was switched off at the beginning, but I came through," He added about the McKenzie fight. "I took his best punches and it was amazing to people how I got up.
"But I've got two lovely kids at home and that is the reason I got off the floor and why I do what I do - that is what pushes me to succeed.
"I'm looking forward to this rematch and doing the business. The bout with Cleverly is within touching distance, but I have to come through July 16.
"It means nothing if I don't come through this next fight. My full focus is on McKenzie and then we can start talking about Nathan Cleverly."
