Luis Suarez was brought down by Lukas Podolski in the second half, with Steven Gerrard converting from the spot to pull the Reds back into the game.
But Suarez was denied a second spot-kick just a few minutes later after going down under a strong challenge from Alex Oxlade-Chamberlain, much to the dismay of Rodgers.
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"I'm not sure if it's because it was just after that but it was certainly a clear penalty. Luis has just got a touch on the ball and Alex has just taken him inside the box in front of the referee's eyes, so it was a strange decision."
Rodgers felt his side were worthy of a place in the quarter-finals despite narrowly falling short at the Emirates Stadium.
"I thought the best team lost," he added. "I thought the very least we deserved was a replay in the game, and probably should have been 2-0 up in those first six or seven minutes.
"I thought going forward we were outstanding [and] created so many chances. I'm disappointed with the goals, the first one in particular is just a long ball into the box. The positioning might have been better for the second one.
"We're bitterly disappointed not to get something and to get another penalty, which I thought was a blatant penalty."