The Reds beat the Latics 2-0 at Anfield thanks to Iago Aspas' first goal for the Merseysiders as well as an own-goal from James Tarkowski, sending them through to the fourth round where they were beaten by Oldham at Boundary Park last season.
In the 83rd minute, Rodgers' 20-year old midfielder son Anton came on for Oldham and he was absolutely thrilled to be involved in a match of this family importance.
"It's brilliant, I've seen Anton's life from when he was a young footballer and to see him run out there was a bit surreal really," Rodgers said.
"He's a great kid and we're very proud of him as mother and father. He's having a good career and Oldham are a brilliant club for him, they really look after him well. They've got an outstanding young manager who will go on to do really well and he's got a young team and they've got a great spirit.
"I've seen them a number of times and Anton's obviously playing a part in that. It's a great moment in his career and, as a father, it's even more special that he gets a nice round of applause from the Liverpool supporters as well."
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