The 20-year-old stopper is set to complete his £20 million switch to Old Trafford in the coming days, having recently won the European Under-21 Championships with Spain.
Currently No.1 at Atletico Madrid, De Gea was quickly promoted from the youth team to the senior side following an injury crisis at the Vicente Calderon.
A last-minute change of heart from the Spanish club scuppered a potential loan move to the DW Stadium, but Martinez is confident De Gea will prove a fine replacement for the retiring Edwin van der Sar.
Speaking to the Evening Post he said: "It's true, we had David signed on a loan deal, but unfortunately on the last day of the transfer window everything fell through.
"The problem wasn't on our side of the agreement - Atletico Madrid just felt he had to stay, and they were proved to be right.
"Shortly afterwards, their two senior goalkeepers got injured, he got an opportunity and he quickly became a hero. And everyone has been able to see for themselves the true quality of David de Gea."
Martinez is also not surprised by the rapid progress of his fellow countryman, and suggested the mooted £20 million price tag will turn out to be a snip.
"We followed him for a long, long time, and we have always known how good he is," he said.
"He has matured so much at such a young age, and the price tag Manchester United are talking about already looks to be a bargain."
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