"It was great to see him in action, I think I was more nervous than AJ", Gazza said.
Joshua's promoter, Eddie Hearn, says a unification fight with Wilder needs to happen in 2018 but does not think the American deserves a 50-50 split.
The only belt missing from Joshua's collection is the WBC belt - held by Deontay Wilder.
Wilder had been due at ringside but didn't show and a confident Joshua, speaking to Sky Sports, after his win was confirmed: "Wilder, let's go baby".
On several occasions, the referee got himself between the fighters when most officials would have allowed them to fight their way out of the exchanges.
Should Joshua and Wilder put off fighting each other, the varying sanctioning bodies might move to strip one of the belts.
My strategy in there was to stick behind the jab. "I think he'll go on to be a better fighter because of tonight's performance".
One area where there was is no danger of anything being lost in communication is which opponent Joshua wants to face next - outspoken WBC champions Deontay Wilder, in order to complete the set of the heavyweight division's major belts. So this does become a boxing match, not a fight.
"I said this would be about boxing finesse".
This result was New Zealand boxer Parker's first defeat in his 25-fight pro career.
"2018 was always the time to capture all the belts and we are one away now", Joshua said in a news conference.
His footwork was much slicker and of course his cardio - despite a little dip in the middle rounds - was mostly excellent as he came on strong in the final frames of his first full quota rounds.
"That was in November, we were told they would get back with a P and L (statement), with the numbers, but we never heard back from them again", Finkel added.
But the CompuBox stats suggest Parker's problem - no doubt influenced by Joshua's longer reach - was precision.
Barry would have liked Parker to throw more combinations in an effort to take Joshua out of his comfort zone.
Parker's raiding attacks continued to unsettle AJ, who was forced to hold in the ninth, but Joshua's spiteful work opened a cut over his foe's eye in the 10th.
Round four followed a similar pattern, then Joshua caught his opponent with a couple of powerful body shots in round five before Parker tried to raise the tempo, and it proved his best spell of a fascinating encounter.
Dillian Whyte and Alexander Povetkin could meet next to hasten their route into a fight against Anthony Joshua. Parker charged out for the sixth, chasing Joshua to the ropes, and both traded big punches as a tense duel turned into a brutal encounter.