Fortunately, the cut, which initially bled down Fury's nose, was well handled by the Englishman's corner and it wasn't a factor, the fight going the full 12 rounds.
As we have seen in recent boxing decisions, and the widely varying views of the fight espoused on social media and elsewhere, a dominant performance doesn't not necessarily translate to victory or universal acceptance, and the judges may have seen things differently had the fight been truncated.
"On reflection it was a great result and a great way to finish this trip," Parker said. "It was a long training camp, a long time away from home. I thought 'damn, if it goes to a decision then he'll get it because it's his hometown' but I'm thankful the judges... I thought it was closer, but I felt I put him under pressure and landed the bigger punches and he ran.
"But he did good - I knew he was awkward but I didn't know he was that awkward."
Parker, looking forward to travelling home to Auckland for a break, added: "It's up there [in terms of achievements] because everything was stacked against us. Fighting here - in his hometown, the judges and ref and all that...
"I don't feel he took a lot of rounds because his jab was a pitter-patter, it was soft. I was catching it."
Wanting a fast and powerful start, Parker got it, but Fury's ability slip away and then lean out of range - particularly when on the ropes - made him a difficult target.
"There are a lot of things I need to work on when I go back into camp," Parker said. "I need to work on my footwork, pressure, more punches to the body, but in every fight you're learning and getting more experience."
Parker's promoter David Higgins will now look at other opportunities - his man may fight again as soon as December - and he hinted that the United Kingdom is where he would like to continue.
"Seriously, the scene is here because there are so many heavyweights. It's booming at the moment."
Parker had walked to the ring in red and black colours, with a "Parker" headband, while the Ka Mate haka made famous by the All Blacks sounded on the loud speakers, eventually the war cry blending into his traditional ring walk music.
With a surprisingly large number of New Zealanders in the crowd, and one or two New Zealand flags waved, it all served to bring the evening to the boil.
"Back home it is awesome because you have the support from everyone," Parker said.
"Coming here, I felt it was important to show them what gets us into the mood. The haka is one of things that everybody knows. It represents New Zealand. My uncles were there to represent Samoa, so I had the whole package."