The Reds took a ninth-minute lead through Emre Can's deflected effort before Gary Cahill levelled five minutes later. Diego Costa's 67th-minute strike sealed victory as the Spain international scored his 10th goal in just his 12th game for the Blues.
However it was the non-award of the penalty by referee Anthony 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.
"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."