It was clear that Haye was struggling physically before his trainer Shane McGuigan threw in the towel in the 11th round at London's O2 Arena, with the 36-year-old suffering a suspected Achilles injury at the halfway point of the bout.
But Bellew told BBC Radio Five Live's Sportsweek programme he was also battling an injury.
He said: "I'm just happy David's home and healthy and safe. We did receive injuries. I broke my right hand in the second or third round. It's very sore now.
"I had a bad right knee myself going in but this is not what people want to hear. This is why I asked David from the very start, 'are you okay?' And believe me for four rounds he was fine."
Bellew said he had put the injury out of his mind during the fight, adding: "I don't feel the pain, all I think about is winning."
The build-up to the fight was dominated by trash-talking between the pair but they were respectful of each other afterwards and a rematch could even be on the cards.
Bellew condemned Haye's threats in the build-up, saying: "I know there's been a lot of bad blood and I think some of the things he said were disgusting and distasteful but it was purely one way.
"I didn't want to hurt David. I would never say I wanted to hurt someone. My 11-year-old son had to listen to someone tell people he was going to decapitate me."
Liverpudlian Bellew must now decide whether to defend his WBC cruiserweight title or remain at heavyweight, where he could seek to become a two-weight world champion.
Bellew said he will take time to assess his future, but promoter Eddie Hearn revealed he had already been approached by the camps of WBC heavyweight champion Deontay Wilder and WBO titlist Joseph Parker.
Hearn said: "I think I got into bed about 3.30am, I had Deontay Wilder's camp phoning me up, I had Joseph Parker's camp phoning me up, both wanting to defend their world heavyweight titles against Tony Bellew. So he's got no end of options.
"He's got big decisions to make - stay at cruiserweight, defend that, unify the division. Maybe even a rematch with David Haye or, I think more likely, to challenge for the world heavyweight title.
"Tony's probably got another two, three, four, five fights. This is a tough sport and it's all about securing your future and your family's future.
"He did that in one fight last night and now it's just a case of carrying on this Cinderella story and see how far it can take us.
"People didn't believe he could beat David Haye, why can't he beat Deontay Wilder, why can't he beat Joseph Parker? I believe he can."