Smith, who was playing for non-league Solihull Moors little more than 18 months ago, bagged a fine double after tormenting the Kop backline and Rodgers was raging.
He said: "The boy Smith hadn't scored a goal at home in two years and he's come up against two big units.
"He's a boy who has come out of university football and he looks like Didier Drogba.
"We have seen it before with Villa's Christian Benteke, who after our game has disappeared. That is the resilience and steel we need to have and we have to do it consistently.
"So Oldham may not have been a big game for one or two of them. But they will learn over the course of time, because if they don't they won't be here - it's as simple as that. It was too soft.
"To play at this level there has to be more demand of players for sure."