Despite his disappointment, Rodgers was keen to congratulate Oldham on their progress into round five, where they'll meet Everton at Boundary Park.
He said: "I thought they did well. If they fight like that, they shouldn't be down where they are in the league.
"Congratulations to Oldham - you cannot take it away from them, as bitterly disappointed as we are. It's a club that has been going through a tough time and a result like that could give them the lift to push on."