A further three fans have reportedly been identified by the club but failed to report to the Sinobo Stadium in the Czech capital after the video - in which they are easily identifiable - spread quickly on social media in the hours before Thursday evening's kick-off.
While on global duty, England's Raheem Sterling, Danny Rose and Callum Hudson-Odoi also faced racial abuse from Montenegro fans during the 5-1 win.
Liverpool kept pushing for an equaliser but an injury time corner from Iago Aspas fell straight to a Chelsea player and they broke up the field for former Liverpool striker Fernando Torres to set up Willian for 2-0.
The statement read: "The video circulating online, showing vile discriminatory chants being aimed at one of our players, is unsafe and disturbing".
The Liverpool manager called their behaviour "disgusting" and said they should be hit with life bans.
Liverpool Football Club believes it is the responsibility of those in positions of authority, following proper process, to act urgently to identify and then punish anyone committing a hate crime.
Utterly Class Lomachenko Floors Crolla With Fourth Round Crushing KO
The fight was promoted by Top Rank Boxing and aired live on the Worldwide Leader in Sports' digital streaming service, ESPN+. A minute into the next round it was all over, Crolla going down just a minute in after a hard right hook from Lomachenko.
There is no place for this behavior in football, there is no place for it in society.
"It is our expectation that this will not be repeated in Liverpool, and where there is evidence of any inappropriate or disrespectful behaviour, we will take the strongest possible action".
Meanwhile, Arsenal's Pierre-Emerick Aubameyang has described the latest incidents of racist abuse in football as "really painful" as he urged the sport to find a way of removing the scourge from the game.
They head into the weekend's Premier League fixture with a crunch game against Chelsea at home, which looks like their last toughest fixture in the league. Records are nice but we have to hold them.
"We enjoyed that day and hopefully we can replicate it on Sunday".
Since Young shifted to the role of full-time defender, he's had the zeal of a convert when it comes to the more - how shall we put this - "physical" aspects of the game. "We encourage supporters to report any incidents as they happen to stewards or via our matchday alert service".
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