Rodgers had made six changes from the team which demolished Norwich 5-0 last weekend but tellingly he left experienced players like Steven Gerrard, Jamie Carragher, Lucas Leiva and Stewart Downing on the bench.
Three changes were made to the back four - although it still had Slovakia international Martin Skrtel at its heart - and they looked helpless to stop Matt Smith scoring twice in the opening 45 minutes.
Rodgers said he wanted to give younger players experience - only Skrtel, Luis Suarez and goalkeeper Brad Jones were aged over 23 - but when the result went against them it was them he criticised.
"We are bitterly disappointed. We started the first half poorly and we started the second half and got punished," he said. "We've got a big week of games but our mentality in that opening period was poor and it ended up costing us.
"I was disappointed with the young players I've got to be honest. We are trying to give them experience and let them see what it was like to play for Liverpool.
"It is not just about playing for Liverpool, you have to be competitive and be part of a group that is going to challenge for trophies.
"I thought how we reacted to that and how we performed, knowing that is what we are looking for, was disappointing.
"It is not enough to play for Liverpool and get up for the Arsenal and Manchester City games (later this week) because if we are going to win trophies you need to be able to come to places like Oldham and win and we weren't good enough for that.
"It is just a different type of football where you have to stand up and be counted. It is great to put young players in but you have to have personality and the young players disappointed."
Things were little better for Oldham boss Paul Dickov despite the win: seven league defeats in their last eight matches have left Oldham 19th in League One, just one point above the relegation zone, with the former Scotland striker not guaranteed to lead the side against Everton in the fifth round next month.
"It's very awkward," Oldham chairman Simon Corney said after the win at Boundary Park.
"We will have to chat about it tomorrow (Monday). Paul has his own decision to make. Days like this are great but the biggest thing is about staying in this division.
"People come up to me now and ask how I can get rid of him after that, but, after the last league defeat, people were asking how can I keep him," the New York-based businessman said.
Dickov, who played for a host of clubs including Arsenal, Manchester City and Leicester City in his career, admitted he was in the dark about his future.
"I very much want to stay and keep taking the club forward," said the diminutive 40-year-old.
"It is a long time since we've had a full house here and I want to bring all those people back again for the Everton tie.
"I don't know if it is enough (to save my job). Let me enjoy this first."
Corney said the windfall will ease the burden on the club.
"Rather than talking about relegation the whole time, it is a massive lift for the club and for the town," he told the club's website.
"The finances are handy but we would have got through the season with or without the cup run. Now we get through it easier."
While Liverpool head to Arsenal for a key Premier League clash on Wednesday, Dickov will be hoping he is travelling on the Oldham team bus for Saturday's League One clash at mid-table Walsall.
Corney expected his players to show a similar commitment at the Bescot Stadium.
"I told the manager it is frustrating that the players proved they are good enough.
"I am not saying necessarily to play like that level week in, week out but certainly to a much higher level than we have been."