The Football Association has confirmed it will take no action against Luis Suarez or Patrice Evra after they did not shake hands at Old Trafford.
Suarez was making his first appearance against Evra following an eight-match ban for racially abusing the Manchester United defender in October.
His refusal to shake hands sparked a half-time confrontation in the tunnel.
Evra added to tensions at the final whistle when he celebrated United's 2-1 victory in front of Suarez.
The FA, which says the refusal to shake hands is not a disciplinary issue, also insisted it has no intention of abandoning handshakes before matches despite the incident.
The governing body added that referee Phil Dowd reported that he dealt with Evra's celebrations at the time and that the tunnel incident was not serious enough to warrant further action.
Although the FA will not sanction Suarez for refusing a handshake, it urged football as a whole to take responsibility for its actions in line with the FA's "Respect" campaign.
Former FA chief executive Mark Palios, speaking on BBC Radio 5 live's Sportsweek, said of the pre-match handshake: "It's clearly symbolic and its symbolism has its place in the game.
"If it can cause more problems in a particular circumstance it's right for the clubs to dispense with it.
"From a player's perspective, it's very difficult to shake someone's hand if you don't want to.
"But players have a responsibility to their club and to the wider interests of the game and it's disappointing if he had agreed to shake his hand."
Manchester United boss Sir Alex Ferguson said after the game at Old Trafford that Suarez's actions could have "caused a riot" and Liverpool should sell him.
Suarez, who issued a formal apology on Sunday, has been widely condemned for failing to put the matter to rest after Liverpool had previously stated he would shake hands with Evra.
Former Reds defender Alan Hansen said the Uruguayan let down the club and manager Kenny Dalglish.
Dalglish, who has been fiercely protective of his player, said he did not see the handshake incident, which saw Manchester United defender Rio Ferdinand also withdraw his hand as Suarez approached him.
The incident comes after the FA recently took steps to "defuse further tensions" between QPR and Chelsea by abandoning the handshake prior to the FA Cup fourth-round tie between the clubs.
QPR defender Anton Ferdinand was expected to refuse a handshake with Chelsea captain John Terry, who has been charged with using racist language towards Ferdinand during Chelsea's 1-0 defeat in October.
Wayne Bridge also chose not to shake Terry's hand before Manchester City's match at Stamford Bridge in March 2010, after Terry was alleged to have had an affair with Bridge's girlfriend.
Jeremy Hunt, Culture, Media and Sport Secretary, described the episode at Old Trafford on Saturday as "incredibly depressing" and said it was up to the FA to scrutinise the matter further.
Hunt told the BBC's Andrew Marr Show: "We've made huge strides in changing football discrimination but the last few weeks show you can never be complacent."
Standard Chartered, the bank who pay around £20m a year to be Liverpool's shirt sponsor, said: "We were very disappointed by Saturday's incident and have discussed our concerns with the club."