Liverpool have moved two supporters from behind the dugout area at Anfield but found no evidence any fans spat at Manchester City’s backroom staff, as had been alleged.
A complaint was made by the visitors following an incident in last month’s 2-2 draw.
However, it is understood there was no mention of being spat at in subsequent interviews and statements received from City staff and the club did not report the incident to police.
Liverpool could find no evidence of spitting in their investigation.
However, they did find aggressive behaviour, in the form of shouting and gestures, by two fans and they have been moved from their seats behind the dugouts.
Full details of the investigation have been passed to the Football Association.
“We have now completed a full and thorough investigation following a complaint of an alleged incident near the dugout area at our fixture against Manchester City at Anfield last month,” said a Liverpool statement.
“The evidence gathered was substantial and included statements from Manchester City’s backroom staff, supporters, stewards, unredacted video footage and CCTV recordings.
“We have followed the club’s official sanctions processes and appropriate actions have been taken based on the evidence gathered and information received from the complainant.
“We would like to thank all parties who have supported this investigation and now consider this matter closed.”