Brendan Rodgers was left angered after referee Anthony Taylor decided not to penalise Gary Cahill's handball even though he had a "clear view of it".
Liverpool ended up on the losing side at Anfield despite taking the lead through Emre Can's deflected shot in the first half.
Cahill equalised, thanks to the help of goal-line technology, before Diego Costa fired the winner, scoring his 10th goal of the season as Chelsea continued their unbeaten start to the season.
However it was the non-award of the penalty by Taylor which was the main talking point, after a shot from Steven Gerrard hit the arm of Cahill in the area late on.
"It was a clear one," Rodgers told BT Sport 1 after the 2-1 defeat.
"We worked so hard in the game, we need those decisions. It was quite obvious, it hits his hand, it was a clear clear penalty and the referee has a clear view of it. The players gave everything and we deserved at least a point."
It was Liverpool's fifth league defeat of the season and Rodgers, who has now not beaten Chelsea in eight attempts, is hoping the return of Daniel Sturridge will be the catalyst to kick-start their season.
"We have got to keep working hard," Rodgers added. "We are hoping Daniel will be back after the international break.
"We understand the frustrations (of the fans), the players, myself and the staff, we have a lot of work to do."
The win saw Chelsea go 15 points clear of the Reds and captain John Terry is hopeful their form, which has seen them go seven clear of second-placed Southampton, continues.
"We have seen that everyone has beaten everyone," he said. "We have had a good run, hopefully we can come back from the international break and continue our form.
"We are proving hard to beat and long may that continue."

Terry conceded that Liverpool should have been awarded a penalty late on, saying "We have had some not go our way, it evens itself out", but for his manager Jose Mourinho, his side's performance was worth the headlines.
"Too far (away) for me (to tell), I don't know, but the victory is very much deserved," he said.
"I know that some people say that Liverpool didn't play so well, I would disagree, they tried everything, but Chelsea were the best team."
ends
Additional reporting from PA
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