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The Uruguay international was given an eight-match ban in December 2011 after the Football Association found him guilty of racially abusing the Manchester United left-back.
"I've made two mistakes in my career. When I was playing for Ajax and I bit [Otman] Bakkal and what I did with [Branislav] Ivanovic [against Chelsea]. Those were my mistakes and I asked for forgiveness," Suarez told Sport890.
"All the other things were like a movie that people in England believed in. Evra? That's what I'm talking about. It wasn't true. I was never accused with real evidence but that's something to forget."
Suarez admits it has been difficult for Liverpool to “protect” him during his controversies but has been buoyed by the support from his team-mates, in particular Steven Gerrard.
“As time goes on, I'm getting more mature and I think better things,” said the striker.
“If I don't feed the journalists, journalists can't speak about me. I'm now focused on football.
“The club, fans and team-mates were great because it's hard to protect someone as they did with me with the way I was behaving. They all supported me, especially my team-mates. If you listen all the bad things, you get depressed, same thing for the good things.
“Gerrard is the guy at Liverpool. He's always backed me up. He talked to the press and me and that's something that will stay with me forever. Same thing for the coach [Brendan Rodgers], I have a great relationship with him.”