"He simply didn't show up," Barry said. "The pressure of the occasion got to him and he was like a deer in the headlights."
Parker was more diplomatic, saying Joshua's performance was impressive.
"Anthony Joshua put on a very powerful and dominating performance. He did what he had to do under pressure to get the victory."
His promoter David Higgins, who was ringside in London with Duco Events business partner Dean Lonergan, was less impressed, however, saying he was thrilled Joshua won because he represented a potentially easier path to the title for Parker.
"Joshua is a right hander, he's orthodox, whereas Martin as a southpaw would always have presented different challenges," Higgins said. "We would be quite comfortable facing Joshua because the British media and public will now talk him up as being the best thing since Lennox Lewis when really he is a lumbering heavyweight. He is slow, Joseph Parker is way quicker."
Barry agreed Parker would have superior hand speed, but was quick to point out the 24-year-old had only one fight on his mind - his impending bout against Paris-based Takam.
"Joe has freakish hand speed, probably the fastest hands in the heavyweight division," Barry said. "If we end up in the ring against Anthony Joshua some time in the future, that would definitely be something we would look to use. Joshua is a big guy. At six foot six, he is an inch-and-a-half taller than Joe and he has an 82-inch reach, Joe's is 77 inches.
"[But] there is only one thing in our mind at the moment and it's not Anthony Joshua, it's Carlos Takam."
Joshua was quick to give notice of his power in the first round against the self-styled "Prince" Charles, who walked to the ring in a crown, landing three solid blows with his right hand.
None of them struck flush, but when they did in the second round, Martin had no answer.
He was sent sprawling twice and while he appeared aware of referee Jean Pierre van Imschoot's count for the second one, he was too slow to react and the official had no choice but to award the fight to Joshua by KO.
Martin left the ring defeated, losing in his first defence of the title he won almost by default against the injured Vyacheslav Glazkov, but also considerably wealthier. Boxing is on a high in Britain at the moment, and with Joshua and Tyson Fury the holders of three of the world's heavyweight titles, it is also a lucrative industry in which to be involved.