Liverpool striker Suarez and United captain Evra were involved in a series of explosive confrontations on Saturday as they came face to face for the first time since Suarez was given an eight-match suspension for racially abusing Evra during a match at Anfield in October.
Players from both clubs were involved in a heated exchange in the tunnel at half-time of United's 2-1 win on Saturday after Evra reportedly tried to confront Uruguay international Suarez over the handshake snub.
French defender Evra was also spoken to by referee Phil Dowd after the final whistle for his wild celebrations in front of Suarez.
However, the FA say Suarez's refusal to shake hands is not a disciplinary issue, while Dowd has reported that he dealt with Evra at the time and that the tunnel incident was not serious enough to warrant any further action.
Suarez on Sunday apologised for his refusal to shake hands with Evra, but that couldn't prevent Liverpool chiefs condemning their star striker.
Reds manager Kenny Dalglish and managing director Ian Ayre both claimed Suarez had let the club down by telling them he would shake hands with Evra and then changing his mind on the pitch.
Their strongly worded statements came after Liverpool were subjected to wide-spread criticism for both their handling of the Suarez case and Dalglish's failure in a post-match interview to condemn the Uruguayan's handshake snub.
The pre-match handshake routine takes place before every Premier League and FA Cup match and is part of the FA's Respect campaign.
The Premier League had ruled out scrapping the routine for the match, the first time Evra and Suarez have come face to face since the original incident in October, saying to do so would negate the point of the handshakes.
