Liverpool decided not to appeal against the Football Association suspension and £40,000 fine imposed on the Uruguay forward for his comments towards Evra during October's 1-1 Barclays Premier League draw at Anfield, although the Merseyside club continued to challenge the independent commission's findings.
Suarez said in a statement he would carry out the suspension "with the resignation of someone who hasn't done anything wrong" as the word 'negro' - which he claims he used "only once" - is a commonly-used word which does not show any lack of respect in his country.
He has now apologised for any offence caused - although not directly to Evra.
Quoted in several national newspapers, Suarez said: "I admitted to the commission that I said a word in Spanish once and only once. I told the panel members that I will not use it again on a football pitch in England.
"I never, ever used this word in a derogatory way and if it offends anyone then I want to apologise for that."
Manager Kenny Dalglish refused to back down in the long-running row over how the situation has been handled and claimed the 115-page report which damned Suarez's evidence failed to mention several salient facts.
He would not elaborate on what those where but insisted he was right to raise the issue.
Professional Footballers' Association chief executive Gordon Taylor, meanwhile, believes the punishment meted out to Suarez sends a warning that racism in the game will not be tolerated.
He said: "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.
"We have got probably the most multi-cultural 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.
"Some issues are bigger than a player, the club or the game and racism is one of those. We have to learn from it and there should be no misunderstanding or ambiguity in the future.
"You don't want such issues to divide clubs or society. We're all in a football family but we're all under the law of the land.
"Once a penalty has been paid and carried out we move on in a positive manner to make sure the penalty acts as a deterrent. The educational process continues."
Taylor is pleased the authorities in this country take the subject of racism more seriously than FIFA president Sepp Blatter, who last year suggested racism on the pitch should be settled by a handshake.
Taylor added on Sky Sports News: "We've treated it a lot more seriously than that.
"Racism is a serious issue. There was a big court case yesterday which proved that and we want sport to set the best possible example.
"I was disappointed after Sepp Blatter's comment but there wasn't the same outcry in the rest of the world.
"We all know the word 'negro' can be taken to mean a very inflammatory word.
"Any reference to the colour of a person's skin has to be eradicated. In the heat of battle things can be said, but sometimes they go beyond what's acceptable.
"We have had 20 or 30 years of campaigning against racism. I hope we can move on from this and learn our lessons."