Mohamed Salah and Philippe Coutinho put the Reds into a two-goal lead before Shinji Okazaki pulled a goal back before the break.
Jordan Henderson's second-half strike proved decisive as Jamie Vardy immediate reduced the deficit before seeing his penalty saved by Simon Mignolet.
Relive all the action from the King Power Stadium with Sports Mole's live text commentary.
Subs: Gray, Iborra, Hamer, Iheanacho, Slimani, Amartey, Fuchs
LIVERPOOL XI: Mignolet; Gomez, Matip, Lovren, Moreno; Wijnaldum, Henderson, Can; Coutinho, Firmino, Salah
Subs: Oxlade-Chamberlain, Karius, Sturridge, Solanke, Milner, Klavan, Alexander-Arnold
The former Borussia Dortmund coach told reporters: "It sounds like we have no points and are completely the worst team in the league. Yes we have problems, that is why we 'only' have eight points and not 15. We can make it more serious than it is or we can take it like it is.
"I know already about all these problems - or 'not problems' - and I've made my decision already how to work with it, but if I talk a lot about it I only create headlines and it doesn't help us."
He told LCFCTV: "It was clear to see that their manager wasn't happy after the game, so he'll be rallying them up.
"They'll want a reaction, but we've got to not just match that, but outdo that. We have to make sure that Tuesday was a momentum changer for us so that we get back into that winning habit again."
5 - Jamie Vardy has scored five goals in his last three PL games against Liverpool, including two braces at the King Power Stadium. Thorn. pic.twitter.com/vv8Klmb83y— OptaJoe (@OptaJoe) 23 September 2017
16 - Philippe Coutinho has scored more goals from outside the box than any other player in the @premierleague since his debut. Skill.— OptaJoe (@OptaJoe) 23 September 2017