"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."