Premier League - Suarez and Dalglish apologise for behaviour
Suarez snubbed Evra before Saturday's Premier League match at Old Trafford, receiving widespread condemnation.
The Uruguayan has recently returned from an eight-match ban after an FA Independent Commission found him guilty of racially abusing Evra.
The 25-year-old said: "I have spoken with the manager since the game at Old Trafford and I realise I got things wrong.
"I've not only let him down, but also the club and what it stands for and I'm sorry. I made a mistake and I regret what happened.
"I should have shaken Patrice Evra's hand before the game and I want to apologise for my actions.
"I would like to put this whole issue behind me and concentrate on playing football."
Liverpool managing director Ian Ayre said: "We are extremely disappointed Luis Suarez did not shake hands with Patrice Evra before yesterday's game. The player had told us beforehand that he would, but then chose not to do so.
"He was wrong to mislead us and wrong not to offer his hand to Patrice Evra. He has not only let himself down, but also Kenny Dalglish, his team-mates and the Club. It has been made absolutely clear to Luis Suarez that his behaviour was not acceptable.
"Luis Suarez has now apologised for his actions which was the right thing to do. However, all of us have a duty to behave in a responsible manner and we hope that he now understands what is expected of anyone representing Liverpool Football Club."
Dalglish had said on Thursday he expected Suarez to shake Evra's hand, but reacted angrily when questioned about the incident after United's 2-1 victory.
He told a Sky Sports interviewer: "I think you're very severe and I think you're bang out of order to blame Luis Suarez for anything that happened here today."
However, he has now said sorry, commenting: "Ian Ayre has made the club's position absolutely clear and it is right that Luis Suarez has now apologised for what happened at Old Trafford.
"To be honest, I was shocked to hear that the player had not shaken hands having been told earlier in the week that he would do.
"But as Ian said earlier, all of us have a responsibility to represent this club in a fit and proper manner and that applies equally to me as Liverpool manager.
"When I went on TV after yesterday's game I hadn't seen what had happened, but I did not conduct myself in a way befitting of a Liverpool manager during that interview and I'd like to apologise for that."
United issued a statement accepting the apologies: "Manchester United thanks Liverpool for the apologies issued following Saturday's game.
"Everyone at Old Trafford wants to move on from this. The history of our two great clubs is one of success and rivalry unparalleled in British football.
"That should be the focus in the future of all those who love the clubs."
Manager Sir Alex Ferguson said after the match that Liverpool should axe Suarez.
He said: "He's a disgrace to Liverpool Football Club, that certain player should not be allowed to play for Liverpool again.
"The history that club's got and he does that and in a situation like today could have caused a riot. I was really disappointed in that guy, it was terrible what he did."