Luis Suárez cancelled out Matt Smith’s third-minute opener before the Oldham striker netted his second of the game on the stroke of half-time.
Paul Dickov’s side extended their lead courtesy of Reece Wabara’s looping header in the 47th minute, before Joe Allen reducing the deficit to a single goal.
But even Gerrard’s introduction was insufficient to rescue a fourth-round replay, with the England and Liverpool skipper crashing a long-range shot against the crossbar in added time.
“Our mentality was poor and it ended up costing us,” Rodgers said. “But I was really disappointed with our young players.
“We are trying to give them 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.
“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.
“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.”
Get enhanced odds of 18/1 on Andy Murray to win Wimbledon or 10/1 on Novak Djokovic when you open a Paddy Power account.