For Joseph Parker, the morning after the night before had him spending time with family, including baby daughter Elizabeth, and fielding messages of support, including one from Englishman Tony Bellew, whom the New Zealander would love to fight next.

The feeling is mutual after Parker was forced to go the full 12 rounds against Romanian Razvan Cojanu in the first defence of his WBO world heavyweight title, and it seems the only hurdle to a fight between the pair in the United Kingdom in three or four months is Hughie Fury's claim as mandatory challenger.

Parker's promoter David Higgins hopes to have clarity in terms of the next step for the 25-year-old in the next three weeks or so, which means Parker, who will spend about a month in New Zealand, is likely to have an opponent in mind when he returns to his Las Vegas base.

Parker's inability to stop Cojanu at Manukau's Vodafone Events Centre, or even hurt him, has critics emboldened and some of his supporters deflated, but Parker yesterday emphasised that while he was disappointed with his performance, which he rated a six out of 10, it would be foolish to judge him on it.

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"I know I can do a lot better and I know I could have stopped him, but for some reason, it wasn't clicking as well as it should have," Parker told the Herald yesterday.

"A lot of people are going to question me - how I fight and what level I'm at - but it doesn't really bother me. I know I can do a lot better - it's a constant improvement."

As predicted by Parker's trainer Kevin Barry, Bellew immediately re-stated his intention to relieve Parker of his world championship belt, and Dillian Whyte, a heavyweight who was an analyst on the United Kingdom's live broadcast of the fight, wrote: "I don't rate Joe Parker, please make this fight please please."

To an extent, nothing really has changed for Parker. A devastating stoppage of Cojanu might have increased his profile slightly in the UK, and it would have been a confidence booster for him, but the key is the retention of his WBO world title belt; that's what makes him a drawcard as far as fights are concerned.

"I'll fight any of those guys," Parker said. "If you're going to rate me and judge me on that performance, then good. I look forward to jumping in the ring and showing them; hopefully in those fights, I click a lot better and throw a lot more combinations.

"We worked on a few things, including a bigger output, but for some reason, it didn't happen. Maybe I was overthinking. But I like it when they talk about myself and the team, it just gives us extra motivation and drive. I think the best opponent for me next would be Tony Bellew.

"It would be a great fight to have in the UK as a sort of establishment fight. He's a tough competitor and I feel like if we get in the ring, we'll both give it our best. There is respect - we call each other out on twitter but we also send messages. He said 'congratulations and I look forward to doing something together soon'. I feel like I can beat him. If we get in the ring, I think I'll show what heavyweights can do."

There is a belief that while Parker did superbly well to battle back and finish over the top of Andy Ruiz Jr in his world title victory last December (another 12-rounder), his last truly great performance was in the devastating round-three knockout of Alexander Dimitrenko two months before that.

Parker said that form was within his grasp.

"My body prefers a seven- to eight-week camp. That camp was the best camp I've had. The body had the right time to train and prepare. This fight was 12 to 14 weeks [in camp]. The longer the camp is, the worse it is for the body; just more pain here and there. I can easily pull that Dimitrenko form back and display that in the next fight."