Although he admitted the Gunners were the better side at the Emirates, Rodgers felt things could have been different had Jordan Henderson's potential equaliser been allowed to stand.
After being pushed over by Bacary Sagna, Luis Suarez took a quick free-kick which led to Daniel Sturridge playing Henderson in for a tap-in.
But Atkinson pulled play back and instead booked the Arsenal defender, leaving Rodgers in disbelief on the touchline.
Rodgers said: "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.
"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.
"I thought it was a poor decision because you have to let the game flow, but that was the reason he gave it. It was clever play (from us), and we got a goal from it."