Suarez was playing with the Reds in 2011 when he was banned for eight games and fined for racially abusing Evra.
"In the end, he admitted it and he was banned for eight games, and he had a massive fine. I remember after that, Liverpool played a game and they all wore the T-shirts saying 'support Suarez'. He had been banned for racist abuse, had been fined and they support him that way. I was confused and upset," Evra told the official Manchester United podcast.
"But, when I did the punditry on Sky and Jamie Carragher apologised after eight years, I was so surprised. He said they made a big mistake that day and he apologised. It really touched me and now I will respect Liverpool as a football club because, when this happened, I was really disappointed with the club.
"I received an email from the chairman of Liverpool apologising for what happened nine years ago. He said I was welcome to come to Liverpool if I need anything. It really touched me because it's better late than never, but I was surprised that Liverpool supported that kind of attitude."