Brendan Rodgers felt Chelsea playmaker Cesc Fabregas should have been sent off in the opening minute as his Liverpool side's Champions League hopes were all but ended at Stamford Bridge.
The Reds needed to inflict Chelsea's first home loss in the league this season to keep their slim chances of qualifying for the Champions League alive, but are six points behind fourth-placed Manchester United with two games to play and a goal difference of 14 to overcome.
Europa League football is likely at Anfield next term, but Rodgers praised his players for their response to going behind, reserving his frustration for referee Andre Marriner's decision to only book Fabregas for a reckless centre-circle lunge on Raheem Sterling.
"It was a poor challenge. Fabregas should've been sent off - out of control, diving, stretching," Rodgers said.
"It was early in the game (but) it doesn't matter if it's early, beginning of the second half, end of the game. It was a bad challenge and he deserved a red card for it."