Two goals from Matt Smith helped the underdogs to victory, but Rodgers claims that his defenders did not stand up to the physical challenge.
"The boy Smith hadn't scored a goal at home in two years," Rodgers told The Independent. "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 has disappeared.
"Going to places like Oldham, you know what you're going to get. You have to roll your sleeves up and fight, and as I said, it was too soft. That's the resilience and steel we need to have consistently."
Liverpool's next match is against Arsenal on Wednesday evening.