With the Gunners leading 1-0 at the Emirates Stadium, Daniel Sturridge squared for Henderson to tap in after Liverpool had taken a quick free kick, but referee Martin Atkinson pulled the play back to book Bacary Sagna for the original foul.
Rodgers did not understand why Atkinson could not wait until after the Reds attacked to show Sagna the yellow card, and thus allow Henderson's goal to stand.
"That was a poor decision. I think you've got to let the game flow. If that's the ruling, then it's not a ruling that is very good," the Reds manager told reporters.
"We're always asking players to be honest and get up and play, not roll about on the floor, and if they are going to be discouraged from doing that, then they might stay and roll about, try to get someone a yellow card.
"I got an explanation from the fourth official on it, and it is disappointing, to be honest. He said it was the next phase of the game, so he was given a yellow card, and it could only have been given at that point."
Rodgers confessed in the aftermath of their defeat on Saturday that Arsenal were the better team.