Suarez was banned for eight matches following the incident and Liverpool wore t shirts ahead of their next match after the verdict had been handed down to show support for their ex-forward.
However, during a Sky Sports broadcast in October 2019, former Liverpool defender Jamie Carragher apologised to Evra for the incident and the Frenchman said Liverpool reached out shortly after.
Evra was a guest once again on Sky Sports for the clash between Liverpool and United, and was asked if the Anfield club had contacted him, to which the five-time Premier League winner replied: "Yes.
"First of all I was really pleased that Jamie Carragher apologised and, of course, I received a personal letter from Peter Moore and I was really touched about it.
"He told he me hoped it's never too late because this incident happened nine years ago, but I'm someone really positive."
Asked by fellow pundit Graeme Souness if this was a recent incident, Evra added: "I would say three days after the show, and I was like: 'Thank you very much, this letter is really touching my heart.'
"I received a personal letter from Peter Moore. He said he hopes it's never too late. Now I see it's real honest people working for this club."— Sky Sports Premier League (@SkySportsPL) January 19, 2020
Patrice Evra reveals Liverpool sent him an apology for the handling of the Suarez-racism row, after his last Super Sunday appearance. pic.twitter.com/UrctWQRZHk
"I was really disappointed as such a big club as Liverpool to support a big cause like that, but now I can see it's real people, honest people working for this club and I even get more respect for Liverpool because they are fighting against problems of the human race.
"So I was really pleased. It was really important for me. Even though we have a big rivalry for us, this showed you Liverpool is a top, class club."