Luis Suarez's first meeting with Patrice Evra since he snubbed a handshake offer at Old Trafford in February would be reason enough for concern. However, tensions will be even higher due to it being the first game at Anfield since the damning judgement on the Hillsborough tragedy was released last week.
"After what has gone on there is added responsibility on the players for everything to go smoothly," Carrick said.
"We will be doing our utmost to make sure that is the case. It is a heated game because it is a great football match. That is what should be celebrated really.
"It is a rivalry of two great clubs with great histories and traditions. It is what makes the game so special, a classic game worldwide. Hopefully it will be a cracking game of football because it is vital after Sunday everyone is talking about the football."
Manager Sir Alex Ferguson has already urged United supporters to behave, as have the Manchester United Supporters Trust. Now the popular Stretford End Flags group have followed suit.
"During Sunday's visit, Liverpool FC will be paying respect to the 96 victims of the 1989 Hillsborough tragedy, following the release of new evidence last week," read a statement on their website stretfordendflags.com.
"Stretford End Flags support Sir Alex Ferguson's calls for Manchester United supporters to respect this occasion and to further refrain from indulging in the type of chants that have been highlighted by the media over the last week.
"We are led to believe that both Liverpool FC's own stewards and local police will be monitoring the behaviour of both clubs' supporters and anyone participating in chants of a derogatory nature run the risk of both ejection and banning from other games."
Meanwhile, Rio Ferdinand is expected to be recalled as Nemanja Vidic's defensive partner, whilst Paul Scholes' involvement in the last two games suggests the best he can hope for is a place on the bench. That means either Tom Cleverley or Ryan Giggs will occupy the central midfield role.