Anthony Joshua says it was an "honour" to share the ring with New Zealand heavyweight Joseph Parker but his promoter Eddie Hearn has ruled out a rematch following the Brit's victory in Cardiff.

Unbeaten Joshua (21-0) added Parker's WBO heavyweight crown to his IBF, WBA and IBO titles by unanimous decision at the Principality Stadium on Saturday.

While Parker's promoter David Higgins suggested fans would "demand" a rematch, Hearn was quick to hose down the idea as an ultimate unification bout against American WBC champion Deontay Wilder looms for his charge.

Victory over Wilder in a fight mooted for London's Wembley Stadium in the northern summer would make Joshua the first undisputed world champion since Lennox Lewis in 2000.

"Yeah, definitely," Hearn said when asked if a rematch with Parker was off the table.

"But he is going to come again. He wasn't good enough tonight but he's a very good fighter. We need people like Joseph Parker in the division. The more people that are active and are good quality heavyweights the better."

Joshua, who said he spoke to Parker's mother Sala before she left the stadium, also paid tribute to the Aucklander.

"Joseph played a massive part in this, his whole team did and I'm honoured to share the ring with him," he said. "They came, they stepped up, they tried and they'll live to fight another day."

"Joseph won't give up now, he's still young. I think we'll definitely see Joseph Parker again."

Parker and his team took issue with referee Giuseppe Quartarone, even claiming the Italian couldn't speak English, but Joshua wasn't having a bar of it.

"Sometimes the judges get complaints, sometimes the ref gets a hard time from fans and fighters but I don't really like to put a bad name on refs and judges because they're there to do their job," Joshua said.

"Parker's trainer should have advised him of ways to avoid getting disciplined, that's his job. Not to go against the referee but to find a way around the referee and what he's doing."