"I landed some big shots and Kali's a warrior. He came prepared and some of the punches I threw in the first round usually knocks out people and hurts them."
He was confident the result had changed his opponent's opinion of his power, after Meehan commented pre-fight that his 20-year-old son and training partner, Willis, possessed a stronger punch.
Despite talk and expectations that Meehan could take him the distance, Parker said he was always confident of completing the job early.
"I'm sure he does (rate his punching power). I wasn't surprised (at the quick result). We trained hard for 12 rounds but as (trainer) Kevin's (Barry) telling me all the time after every fight, if you see the opportunity, take it. And the opportunity presented itself and I took it."
Parker started the fight well but his enthusiasm to land the big punch saw him deviate from his plans to remain patient, before Barry reminded him of their strategy following a dynamic first round.
Click below for a photo gallery of the fight.
"Joe probably was a little too excited, I had to slow him down and cool him down," said Barry. "I said to him 'come on mate, slow things down, the knock out will come, just get back in behind your jab'".
Parker heeded his mentor's advice and rectified his approach, picking his options and paying more attention to working Meehan's body in the second round to help set up a swift finish.
"That was mentioned to Joe after the first round," said Barry. "It was part of our game plan to go to the body and slow Kali down early and you saw Joe land some vicious body shots in the second round and he did hurt him."
With another fight scheduled for December 5 in Hamilton, and a January bout in Samoa soon to be confirmed, Parker looks set to continue his momentum towards a world title challenge.
"I'm excited for Samoa. But first of all we've got to get through Fight for Life and the next training camp that we have. When we get back to Vegas me and (training partner) Izu (Ugonoh) are going to put in the work and I'll prepare for the next fight."