The English Football Association have pledged to investigate Evra's claims in the French media that Suarez directed racist insults at him throughout the match.
Referee Andre Marriner was seen talking to both players after a clash at a second-half corner and France left-back Evra was later booked for dissent.
The official has included Evra's allegations in his official match report, but Uruguay international Suarez maintains his innocence.
Writing on his official Facebook page, Suarez said: "I'm upset by the acusations (sic) of racism. I can only say that I have always respected and respect everybody. We are all the same.
"I go to the field with the maximum illusion of a little child who enjoys what he does, not to create conflicts."
Evra was determined to draw attention to Suarez's alleged comments and he told French TV channel Canal Plus: "I was very upset. In 2011 you can't say things like this. He knows what he said, the ref knows it, it will come out.
"I won’t repeat what he said, but it was a racist word, and he said it more than ten times.
"He tried to wind me up. I won't make a huge deal out of it, but it's very upsetting and disappointing."
Suarez, who joined Liverpool from Dutch club Ajax for £22 million in January, is no stranger to controversy.
He earned global condemnation at last year's World Cup by handling a goalbound effort by Ghana in the final moments of the quarter-final, then celebrating when the resulting penalty was missed and Uruguay went through on a penalty shoot-out.
He has also been subjected to accusations of diving but Liverpool were keen to defend their player immediately after Evra made his racism claims.
A Liverpool spokesman said: "The first we knew about these allegations was 20 minutes after the final whistle when the manager (Kenny Dalglish) was asked to go into the referee’s office and told about them.
"The first thing we did, as you would expect, is ask the player and he has categorically denied using any language of that nature."
The FA are determined to get to the bottom of the matter.
"The FA has been made aware of an incident that is alleged to have occurred during the Liverpool versus Manchester United fixture at Anfield," said a statement.
"Referee Andre Marriner was made aware of the allegation at the end of the fixture and has subsequently reported this to the FA. The FA will now be making enquiries into the matter."