The Uruguayan, who was banned for eight matches after racially abusing Evra during the league game between the sides at Anfield in October, had been expected to shake hands with the Frenchman but failed to do so, causing an angry reaction from Evra.
Suarez has now said sorry for his actions.
Flashpoint: Luis Suarez refused to shake Patrice Evra's hand
Praise me: Evra (right) made a point of celebrating wildly at the final whistle
'We are extremely disappointed Luis Suarez did not shake hands with Patrice Evra before yesterday's game,' he said. 'The player had told us beforehand that he would, but then chose not to do so.
'He was wrong to mislead us and wrong not to offer his hand to Patrice Evra. He has not only let himself down, but also Kenny Dalglish, his teammates and the club. It has been made absolutely clear to Luis Suarez that his behaviour was not acceptable.
'Luis Suarez has now apologised for his actions which was the right thing to do. However, all of us have a duty to behave in a responsible manner and we hope that he now understands what is expected of anyone representing Liverpool Football Club.'