The club accused some Reds supporters of “wholly unacceptable” behaviour after a mass gathering in the city centre on Friday night led to what police described as a “significant disorder”.
A fire was put out at the Liver Building, while 34 people were injured, three seriously.
And Klopp conceded he “did not love” the scenes on Friday, while informing supporters that they “owe it to the most vulnerable” not to do this.
“I am a human being and your passion is also my passion, but right now the most important thing is that we do not have these kind of public gatherings,” Klopp said in an open letter in the Liverpool Echo.
“We owe it to the most vulnerable in our community, to the health workers who have given so much and whom we have applauded, and to the police and local authorities who help us as a club not to do this.
“Please – celebrate – but celebrate in a safe way and in private settings, whereby we do not risk spreading this awful disease further in our community.”
Both the club and Mayor Joe Anderson have condemned the behaviour of supporters, with Klopp underlining the importance of not “wasting” the efforts to combat Covid-19.
“If things were different I would love nothing more than to celebrate together,” Klopp added. “To have a parade that would be even bigger than the one after we won the Champions League last year, so that we could all share this special moment, but it just is not possible.
“We have all done so much to fight Covid-19 and this effort cannot go to waste.
“When the time is right we will celebrate. But for now, please stay at home as much as possible.”