Forward Luis Suarez apologised on Sunday for not shaking opponent Patrice Evra's hand before his team's 2-1 defeat at Manchester United and manager Kenny Dalglish also said sorry for his post-match reaction when challenged over the snub.
NEWS:Suarez and Dalglish issue apologies
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Suarez was returning to the Liverpool starting line-up for the first time since serving an eight-match ban for racially abusing Evra during a match in October.
Standard Chartered, a bank which pays around 20 million pounds a season to sponsor the former English champions, went public with its criticism in a brief statement,
"We were very disappointed by Saturday's incident and have discussed our concerns with the club," the bank said in a statement.
A person familiar with the matter said: "It was a very robust conversation."
Europe's largest football clubs are now major brands who attract international sponsors and have fans around the globe.
Standard Chartered was attracted to Liverpool by its strong Asian support base. The bank is based in London but makes almost all its profits in Asia. Most of its staff are in Asia, Africa and the Middle East.
The BBC reported that the Fenway Sports Group, the U.S. group that bought the club in 2010 and also owns the Boston Red Sox baseball team, had said an apology was necessary.
A spokesman for Liverpool declined to comment on the reports that pressure had been brought to bear.
The English Football Association, which imposed the original eight-match ban, will take no action over Suarez's refusal to shake hands because it is not a disciplinary issue.
The British government will host a summit in the next few weeks to discuss the issue of racism in football after two high-profile stories this season.
Chelsea captain John Terry will go on trial in July accused of racially abusing opponent Anton Ferdinand during an on-pitch row in a Premier League match in October.
Terry, who denies wrongdoing, has been stripped of the England captaincy for the Euro 2012 tournament and manager Fabio Capello quit as a result.
