"He's awkward and he moves well, he uses the ring well so it was hard to corner and catch him. I rocked him a few times. I give him credit for his movement, it was good.
"I was trying for the knockout, maybe I was trying too hard, so I guess there's a lot to work on. I'll enjoy this victory and celebrate with the team but there's a lot to work on."
Promoter David Higgins was vocal before the fight, Parker's second title defence, about his concerns regarding Terry O'Connor, the man originally slated to be the referee before a late change put fellow Brit Marcus McDonnell in the ring and O'Connor on the judges' panel.
And, significantly, O'Connor was one of the judges who scored the fight overwhelmingly for Parker.
"Everything was against us heading in... I'm just relieved we got the win," Higgins said. "I think I should pay credit to the British Board of Boxing Control because they were very straight.
"We have a voluntary now not a mandatory, which means instead of being forced into one fight we can negotiate a series of deals at the same time and on our terms."
Parker will probably fight again in December, and possibly in London, although Higgins wanted to keep his options open. They included a possible fight in Tokyo or the United States.
Englishman Dillian Whyte wasted little time in calling out Parker on Twitter. Higgins said: "It's all risk and return. Look, Dillian Whyte calls everyone out every week."
Fury, who suffered his first loss in 21 professional fights, promised to be awkward and he certainly was. His height allowed him to sway out of the range of Parker's big shots, but he was caught several times and a cut opened above his right eye in the fourth round.
Parker was never hurt and again didn't suffer any marking to his face.
Trainer Kevin Barry said: "I thought Joe threw a couple of really good punches in the first round which set the scene for the night. Hughie realised he couldn't stand there ... if he was going to survive.
"What this does now is it sets the scene for us to do business in the UK."
Parker, who arrived to the ring to big cheers from a surprisingly large Kiwi contingent in the audience, planned to celebrate quietly with friends and family afterwards.
"Just relax with the team," he said. "It's not just effort from myself, it's effort from the team. There are a lot of people who travelled here to watch me fight and support me - New Zealand, Vegas, Hong Kong, so we'll get together and celebrate."