Former Manchester United captain Neville had described Romero and Martinez as "the best, worst centre-half pairing in the world" in his build-up analysis ahead of Argentina's dramatic 2-1 semi-final win over England. Both defenders were booked during the feisty last-four match in Atlanta, but they also helped restrict England to just two shots on target as the defending champions came from behind to win with two late goals.
Asked about Neville's comments by DSports, Tottenham defender Romero did not hold back.
"The only thing that I hope for is that when I retire, I am not that stupid. Hopefully I won't criticise a player or anyone," he said. "Because at the end of the day, we are doing our best for our national team.
"Sometimes it goes right for us, sometimes badly, but we are just happy to be in a World Cup final again. I think we are making history, for us it is something really huge, and we feel the significance of this shirt like no-one else."
Martinez, who plays his club football at Manchester United, offered a calmer response to the same question, framing the criticism as part of the territory that comes with being a well-known partnership.
"We're used to people always talking about us," he said. "It seems like they like doing it, and we respond on the pitch, that's it, always with respect."
Both centre-backs are 28 and have started all but one of Argentina's matches at this summer's World Cup, helping Lionel Scaloni's side reach a second consecutive final after a run that has included extra-time wins over Cape Verde, Egypt and Switzerland in the knockout rounds.
Their partnership has drawn scrutiny throughout the tournament for its combination of aggression and occasional lapses in judgement, with both players regularly picking up bookings, but Scaloni has stuck with the pairing throughout the knockout stages regardless of the outside commentary.
Argentina will now turn their attention to Spain, who beat France 2-0 in the other semi-final and await them in Sunday's final at MetLife Stadium in New Jersey. Victory would make Lionel Scaloni's side the first team since Brazil in 1958 and 1962 to win consecutive World Cups, and Romero and Martinez are expected to once again be at the heart of the defence as they attempt to shut out a Spain side that has conceded only once in seven games so far this tournament.