Liverpool have apologised to Manchester United for the behaviour of their fans during last month's highly-charged FA Cup tie at Anfield.
The club and Merseyside Police have carried out an investigation after a number of incidents where United fans at the Anfield Road end were attacked by home supporters.
There was one incident of human excrement being thrown towards United supporters as well as coins and food being aimed in their direction.
Liverpool stadium and operations manager Ged Poynton has written to United admitting standards of behaviour had 'fallen short' of that expected.
Poynton added in the News of the World: 'We hold our hands up as a club. We deplore what certain fans have done. 'I use the word coward very reservedly but I class anyone who wants to throw a coin or something else when they are leaving as cowards.
'I am ashamed to admit in one case excrement was thrown. How low can you get? We did what we could, we tried to brush people down and compensate those involved.'
Tensions between the rivals had been running higher than usual going into the February 18 match - won 1-0 by Liverpool - after a controversial end to a Premiership encounter between the sides the previous month.
United's Gary Neville had run to celebrate in front of Liverpool fans after Rio Ferdinand headed a later winner at Old Trafford.
The cup tie was also marred by a section of home fans taunting United's Alan Smith after breaking his leg late in the match.