The Premier League's rookie tactician made the headlines after reportedly telling members of the Spanish press that some of his fellow top flight managers were Sir Alex Ferguson loyalists, who often ganged up on his compatriot Rafa Benitez.
Martinez subsequently denied making the comments and Allardyce confirmed that he had phoned him to apologise.
Allardyce, whose team take on Manchester United at Old Trafford on Saturday, accepted Martinez's apology but warned him to be more careful in the future.
"I accept what he said when he rang me," Allardyce said. "When I saw the papers I thought, 'Is it true or isn't it? But I have to take his word for it, which I do.
"Welcome to the Premier League, Roberto. Keep your mouth shut in the future or make sure you remember what is going to be done in the Premier League.
"If they have distorted his words, then that is something of a regular occurrence at this level.
"It's not a real problem for me, I just think Roberto has learnt a harsh lesson about what happens in the Premier League if you start diverting away from you and your club business.
"You can say you can be misinterpreted, you can say you can be read wrong, but it's a lesson that when you comment in this league on anything it can be blown out of all proportion.
"He's apologised to me and I accept that apology."