The seven-times cup winners were roughed up by the third-tier side in a 3-2 defeat on Sunday that prompted the Liverpool manager to question whether some of his young charges had the desire to succeed at the top.
"It hurts deeply and it makes things clear, we need a group that's hungry in every single game," Rodgers was quoted as saying in British newspapers on Tuesday.
"If they don't have that hunger, they will find themselves playing in League One and regretting the opportunity they missed.
"Oldham may not have been a big game for one or two of them but they will learn quickly they have to have the right mentality for every single game, because if they don't, they won't be here, it's as simple as that.
"They are a talented group, but let us be clear... we don't have world-class young players. So they must come in with the intention of working hard with intensity every day. That is the only way they will succeed."
With daunting Premier League trips to Arsenal and Manchester City coming up, Rodgers chose to make several changes to his side for Sunday's fourth round clash, including dropping Steven Gerrard to the bench.
In came defenders Sebastian Coates, 22, and Jack Robinson, 19, to join the 19-year-old Andre Wisdom in a makeshift back line, while 18-year-old Raheem Sterling started in a forward line that was strong on paper but ineffective on the day.
The centre-back pairing of Coates and Martin Skrtel came in for particular criticism after being out-muscled by Oldham's two-goal hero Matt Smith, a 23-year-old, who was playing university football two years ago.
Skrtel has been a mainstay of Liverpool's defence but was dropped for their last Premier League outing against Norwich City and may struggle to stay in the starting line-up for Wednesday's trip to Arsenal.
"The boy Smith hadn't scored a goal at home in two years and he's come up against two big units we have at centre-half [Skrtel and Coates]," Rodgers said.
"He is a boy who has come out of university football and he looks like Didier Drogba.
"We have seen it before with [Christian] Benteke, who after our game against Aston Villa [when he scored twice in a 3-1 win] has disappeared. That's the resilience and steel we need to have and we have to do it consistently.
"Going to places like Oldham, you know what you're going to get. It's not a Premier League game; it's a game where you have to roll your sleeves up and fight and, as I said, it was too soft.
"One or two were too soft, it's as simple as that. I'm talking in general, about the physicality around the team, not just Martin Skrtel. I would expect all the players to react, not just him."
Liverpool are seventh in the Premier League and seven points behind Tottenham Hotspur who occupy the fourth and final Champions League qualification spot.
