The Northern Irishman suggested that Suarez was a 'cheat' and a 'cancer on the game' after the Uruguayan was accused of diving against Stoke City last weekend.
Suarez admitted today on Argentine radio that he was not aware of who Boyce is and wondered why he would need to be making such remarks about someone else.
"This guy [Boyce], I've no idea who he is," said Suarez.
"I don't know why he has been talking about me. He certainly can't be well-known and he wants to get publicity.
"Let him carry on talking. My job is to play football and to try to do so in the best way possible," he added.
"What he has said does not affect me. I am not interested in what he has to say. It's been important to have the support of the Uruguayan FA and the people.
"I have lived through a lot in the past year, with people saying things about me, but I have continued playing and proving my job is what happens on the pitch."