Suarez was banned for eight matches and fined 40,000 pounds (US$62,000) for calling Evra "Negro" or "Negros" seven times in October during a 1-1 draw at Anfield.
The Uruguay international said on Tuesday he would reluctantly accept the punishment while stressing that his comments, in Spanish, during the confrontation had been lost in translation.
The 24-year-old forward has conceded that his conduct might have caused offence but said it was not intended to do so.
"I admitted to the (English Football Association) commission that I said a word in Spanish once, and only once and I told the panel members that I will not use it again on a football pitch in England," Suarez said Wednesday in a statement provided by Liverpool. "I never, ever used this word in a derogatory way and if it offends anyone then I want to apologize for that."
Suarez, though, did not apologize directly to Evra, the black France international whose conduct has been questioned by Liverpool.
Liverpool manager Kenny Dalglish is still incensed by the verdict last month by the disciplinary panel.
"There's a lot of things we'd like to say and a lot we could say, but we would only get ourselves in trouble," Dalglish said on Tuesday. "We are being evasive because we don't like getting ourselves in trouble."
English soccer's anti-racism group hopes the club uses the incident to push an anti-racism message, though the team had been strong in its support of Suarez, with other players wearing T-shirts bearing his image and number in a pre-game warmup.
"We commend Liverpool FC in bringing closure to this matter, reaffirming its commitment to an unequivocal, zero-tolerance approach towards discrimination in football," said Herman Ouseley, chairman of Kick It Out. "The club can now move on from this period, showing leadership in how it demonstrates and communicates this stance to players and fans alike."
The players' union believes Suarez's punishment sends a warning that racism in the game will not be tolerated.
"It's a lesson to all of us ... that all players coming into our game from different countries understand and accept what we are about — equality and diversity," Professional Footballers' Association chief executive Gordon Taylor said. "We have got probably the most multicultural game in the world so it's important to set the right example.
"We don't want him (Evra) feeling a victim. We want our black players to feel comfortable that racism can be dealt with in football terms, as well as the law of the land."