The hosts failed to trouble Chelsea with their only shot on target coming after the 80th minute.
Jurgen Klopp has described the loss as a ‘massive blow’.
“It is not about Anfield or whatever, it is in general, too often. In the decisive moments we have to improve,” Klopp said.
“It was a tight, intense game. It is a massive blow. We have to win football games. It is not done yet.”
Klopp also clarified the the reason he hooked off Mohammed Salah with twenty minutes to go which left the Egyptian stunned.
“I just brought on fresh legs. Mo looked like today he suffered a bit, he played a lot of games.
“I could have taken off Sadio (Mane) or Bobby (Firmino). That is all clear but at that moment it looked like Mo.”
Liverpool will return to Premier League action against Fulham at Anfield on Sunday.