The Uruguayan forward was heavily criticised for his theatrical dive against Stoke, going down dramatically and in stages despite no contact from the nearby Steven N’Zonzi.
And Boyce was at the forefront of that criticism, labelling Suarez’s actions as “nothing less than cheating” and “a cancer within the game”.
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"This guy [Boyce], I've no idea who he is,” an angry Suarez told Uruguayan newspaper Ovacion.
"I don't know why he has been talking about me. He certainly can't be well-known and he wants to get publicity."
Suarez, who played in Uruguay’s Friday night 3-0 loss against Argentina, is determined to let his football do the talking and has deflected the recent criticism.
"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."