The incident is the latest in an ongoing dispute involving both clubs, which came to a head in December when the Liverpool player was handed an eight match ban after being charged by the FA of racially abusing Evra.
The club’s shirt sponsor, who are in the second year of a four year £80m tie-up, signalled its discontent to American owners, Fenway Sports Group.
In a statement it says: “We were very disappointed by Saturday’s incident and have discussed our concerns with the club.”
On Sunday, Liverpool’s managing director, Ian Ayre, manager, Kenny Dalglish and Suarez released separate public apologies following the match. The club claims it was not pressurised into making the public move by its sponsor.
The club said in a statement: “Ian Ayre kept Standard Chartered fully informed of developments over the course of the weekend. The actions the club decided to take on Sunday were supported by Standard Chartered.”
According to reports the bank, which was attracted to the Anfield club because of its strong Asian support base, is concerned that the latest incident could damage its reputation in emerging markets.