The 20-year-old was a roaring success in a season-long loan with the Premier League side, prompting new Barcelona coach Luis Enrique to recall him to the first team ahead of the new season.
Spain coach Vicente del Bosque also noted the youngster's progress with Everton, calling him into the squad for the international friendly with Bolivia at the end of May.
Martinez believes Deulofeu would have got more playing opportunities had he stayed at Everton for one more year rather than returning to Barcelona, where he will be competing for a place in attack with Lionel Messi, Neymar, Pedro and Alexis Sanchez.
However, the Spanish manager believes his former charge can succeed at the Nou Camp.
"He is ready to play for Barcelona because he has special talent, certain qualities that make him stand out," Martinez said in an interview with Spanish national daily sport newspaper Mundo Deportivo.
"I was delighted when Del Bosque called him up for the friendly before the World Cup. They had followed him for the year he was at Everton and were able to see that he was performing to a very high level.
"It would have been good for Gerard and for Everton if he had stayed for us for another year. He would have enjoyed a bigger role in the team than I think he will have at Barcelona because of the competition he will find there.
"It would have been fantastic to have him at Everton for another year, and another year in the Premier League would have made him better prepared to make the jump up to Barcelona, but they didn't want that, and I presume that's because Luis Enrique, who knows him well, knows how good he is."
As well as Deulofeu, Martinez will be without another of his star performers last season, with striker Romelu Lukaku heading back to parent club Chelsea after scoring 15 goals while on loan with Everton.
However, it is believed the Belgium international could follow Deulofeu in heading to Spain, with champions Atletico Madrid tipped to sign him as part of a deal that will see Diego Costa join Jose Mourinho's side.
"Romelu is a bit like Gerard, a great player but a youngster, he arrived in Liverpool without much tactical discipline, but he has improved a lot, without losing any of his physical or technical assets," said Martinez.
"If he ends up going to Atletico, knowing the work of (Atletico coach) Diego Simeone, it will be good for Simeone and for Atletico. I also think his characteristics will suit Simeone, and vice-versa."