"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."
Aside from failing to match the desire of the home team, Liverpool also lost the physical battle, with Oldham centre-forward Matt Smith who ended the game with a dislocated shoulder dominating the defensive pairing of Martin Skrtel and Sebastian Coates.
"We didn't have enough physicality, especially considering we have got two big strong centre-halves." Rodgers said. "We have a 6ft 4in and a 6ft 3in centre-half.
"The big guy Smith did well, but it is not like we haven't played against that big type before.
"We were too much on the back foot early on, you have got to be aggressive. Across the board, we didn't press well enough from the front.
"This was a trophy that we put focus on to go far and now we are out of it. Oldham did well. If they play like that then they shouldn't be down where they are in the league. They had lost seven of their last eight league games."
Liverpool expect to complete the signing of Inter Milan's Brazilian attacking midfielder Philippe Coutinho early this week for £8 million.
Matt Smith ... not your average footballer
Size: 6ft 6in
Background: The father of Matt Smith, who was Oldham's two-goal hero, combined playing for Scottish clubs and Birmingham City with studying medicine and working as a doctor. Matt's half-brother, Jean-Francois, was a professional basketball player in the French Pro A League.
Education: Smith studied at Pate's Grammar School in Cheltenham and in 2011 earned a 2:1 degree in international management with American business studies at Manchester University's business school.
American experience: Played football in America while spending a year of his degree at Arizona State University.
Posh friends: Jack Whitehall played up front with Smith at university. They were a "lethal partnership", the comedian said.
... And he's not a softie: Smith was forced off with a dislocated shoulder but, after having it popped back in, said he was completely fine.