The Reds produced a number of scoring chances throughout the 90 minutes at the Emirates Stadium but could only breach the Gunners defence once when Steven Gerrard converted from the penalty spot.
After the match, Rodgers felt Liverpool were the better side and that their performance at least warranted a draw.
"I thought the best team lost. The very least we deserved was a replay," he said.
"We're disappointed with the goals, apart from that we were a threat, we played with real confidence and belief."
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