Undefeated in 12 professional fights with 10 knockouts, he is definitely on track, trainer Kevin Barry believing Parker will break into the top five in the world this time next year following 12 months of five or six fights.
"It was by far Joe's best performance," Barry said. "He has been showing me glimpses of that all year. I think he showed tonight just how world class he really is and if that doesn't put the shudders into a few heavyweights around the world I don't know what will."
Parker said: "Once I saw his eyes I knew it was a good punch. I looked over at Kevin and he was jumping up and happy."
He added: "He [Costa Junior] wasn't expecting it. It's those punches that you don't expect that get you."
One of the many reasons for this match's hype was that Costa Junior had been beaten only once in 16 previous pro fights, in Germany in October by Christian Hammer, ranked seventh in the world.
Significantly, Hammer failed to do any real damage, winning the fight by decision over 12 rounds.
"We'd fight Hammer tomorrow," Barry said. "You've heard me say this before - there are a lot of guys in the top 10 that I would put Joseph up against immediately."
Barry said of Costa Junior: "You could see the experience of the man because Joe hit him with some huge shots in the first three rounds - most other fighters would have gone down a lot earlier. The one he caught him with was picture perfect. He was out before he hit the canvas."
Parker, preparing to go on holiday in Samoa, was challenged to reach an A-plus rating in his final examination of the year by Barry and can travel feeling comfortable he aced his test.
"We knew once Joe established his jab and got the feint game going there would be holes to the body," said Barry. "I've been taking a few of those body shots from Joe all year and I'm just pleased he threw them on someone else."
Parker, looking forward to celebrating, said with a grin that most of those wayward shots were accidental.
Comfortable indeed.
