Liverpool boss Jurgen Klopp said he had "never celebrated another team dropping points" after Manchester City defender Kyle Walker posted a tweet mocking the Reds' 1-1 draw with Leicester.
Harry Maguire's equaliser prevented Liverpool going seven points clear at the top of the Premier League, a day after City lost 2-1 to Newcastle.
Walker posted a popular meme of Maguire from the World Cup with the caption: "So basically they thought they were gonna go seven points ahead." He deleted it, but it quickly went viral.
City boss Pep Guardiola played down the significance of the tweet, saying: "I'm not concerned about the social media of the players, what they tweet or Instagram, or other social media. I cannot control it."
Klopp said he was not aware of the tweet, but when told about it, said: "I cannot help that. I am not sure what that says about us, it says something more about the other person.
"I never celebrated that another team dropped points or lost a game. For me that's not allowed.
"For supporters it is a little bit different, for people involved I don't understand."
He added: "There will always be a bunch of people who hope you win and another bunch who hope you will lose.
"You have to ignore both in your preparation, and in the end hopefully you celebrate with the ones who want you to win something."
Liverpool are five points clear of City, with 14 games of the season remaining.
At half-time against Leicester, Liverpool groundstaff only cleared snow in the half of the pitch towards the Kop, the end the Reds were set to attack.
But Klopp denied accusations of gamesmanship and said the Anfield workers did not have "enough manpower".
He said: "There was no plan, nobody told them, I can swear, to clear only our side or our box.
"I hear people say it's unsporting, but it's an advantage, if their box is clear then it's better to defend.
"It's no coincidence that in the first half we scored a goal in a box that was full of snow. That's how it is, we cannot change it."