The buildup to the fight had been marked by intense news conferences and heated trash-talk between the British fighters, but after Saturday's fight they quickly put the animosity aside.
"In my eyes I've beaten the best cruiserweight this country has ever produced and one of the best heavyweights," Bellew told Radio 5 live.
"He made the same mistake everybody else does. He underestimated me. Watch me on tape and I'm terrible but in the ring I'm harder to hit than you think."
The 34-year-old Bellew had moved up from cruiserweight to face Haye, whose previous fight was last May against Swiss Arnold Gjergjaj.
Prior to Saturday, Londoner Haye had fought just three times since losing a heavyweight unification bout to Wladimir Klitschko in 2011.
Haye, who has 28 wins from 31 bouts, said his opponent fully deserved the victory but wanted a rematch.
"I would love to do it again, I have never been in a fight like that," he said. "If the fans want to see it again I would do it again.
"We'll do it on his terms, in his town - he deserves it."
Promoter Eddie Hearn, however, said Liverpudlian Bellew (29-2-1) would look for a title shot.
"We've got to go after a heavyweight world title for Bellew now," he said. "He is everything you would want in a man, he has a big heart, never gives up, has a wonderful family and I am so happy for him."
(Writing by Peter Rutherford in Seoul; Editing by John O'Brien)
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