"I think anybody who follows boxing would see this performance and realise they have seen the birth of a superstar," said Arum.
Martinez, who was making the second defence of his title, admitted he was caught out by the speed of the 28-year-old. "I couldn't see his hands," admitted the 33-year-old Martinez.
Lomachenko improved to 6-1 with three knockouts - and became the fastest fighter to gain world titles in two weight divisions.
Japan's Naoya Inoue, a reigning super flyweight titleholder, won a belt in a second division in his eighth pro fight.
Lomachenko, who only lost once in 397 amateur fights, insisted he is still learning the pro game. "I need more fights. It's not enough fights for me. I need fights to get better," he said, adding that he wanted to take on the best of the 130-pound ranks.
"The reason I like Olympic boxing is that all the best fighters come together and find out who the best fighter is. I want to do the same in professional boxing. I want to line up all the best fighters in the 130 division and see who the best fighter is."
Lomachenko won his first world title in June of 2014, dominating former US Olympian Gary Russell to win his in his third pro bout. He matched Saensak Muangsurin's record for fewest fights needed to win a world championship.
The only blemish on his pro record was a loss to Mexico's Orlando Salido in Lomachenko's second professional fight - when the vacant WBO featherweight title on the line.
Salido was ringside at the Theater at Madison Square Garden on Saturday, and Lomachenko said he was game for a rematch. "Let's do it," he said.