The Reds boss handed several young players starts at Boundary Park but saw his side fall to a 3-2 defeat in the fourth round as they were outfought by the League One outfit
The Northern Irishman gave the likes of Jack Robinson, Andre Wisdom and Sebastian Coates an opportunity to start at Boundary Park but saw his side end up on the wrong end of a 3-2 result.
"We were coming here in good form and obviously we are bitterly disappointed," Rodgers told BBC Sport.
"I was bitterly disappointed with the young players as today they had a chance to show they can play for Liverpool and compete for a club that has to challenge for trophies.
"We lost our concentration, and only had spells in the last 35 minutes when we were at the right level. Congratulations to Oldham, though.
"Our mentality was poor and it ended up costing us.
"We are trying to give [young players] experience and let them see what it's like to play for Liverpool, but you've got to be able to be competitive and part of a group that is going to challenge for trophies.
"If you are going to win trophies and go far, then you need to come to places like Oldham and win. We were not good enough.
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"Gerrard has come on with Stewart Downing and, for 35 minutes we were terrific, but it was too late then. We were 3-1 down and it was not good enough.
"But I can't rely on Steven for 70 games. He's been incredible, but he shouldn't be expected to have to come and win games on his own.
"You can't be comfortable at Liverpool. The youngsters are never allowed to be. This is a different type of football to the Premier League and you have to stand up and be counted."