The Ireland assistant suggested the Merseyside club had placed pressure on Seamus Coleman and James McCarthy to make themselves unavailable for the national team.
Neither featured in last month's fixtures with Gibraltar and Germany, but both played in Everton's subsequent 3-0 Premier League win over Aston Villa after that international break.
Midfielder McCarthy also sat out last Friday's 1-0 loss to Scotland with a hamstring complaint, while he and Coleman each missed a friendly clash with the United States on Tuesday.
Everton chairman Bill Kenwright rubbished Keane's claims at the time and Martinez has now made his feelings clear.
"We've got a good relationship with the [Republic of Ireland] manager Martin O'Neill and we keep in touch quite frequently and share information," he stressed. "That's something that, at the club, we're always very proud when our players represent their countries.
"It's something that we're very, very proud of and every player at our club is desperately proud to represent their country.
"A lot has been said. A lot has been nonsense. The reality is that the conversations between the managers of the associations and ourselves as a club have always been really good and they'll carry on being good.
"The only thing I care about is the players. We produced four players for the Republic of Ireland [Coleman, McCarthy, Darron Gibson and Aiden McGeady]... four players who love to play for their country.
"It's disappointing when you see some sort of news in the media that they could put that in doubt. That's the disappointing aspect.
"All the fans of the Republic of Ireland and any nation need to know that these players would give their lives to represent their countries."
