Liverpool were 2-0 up with seven minutes remaining of their FA Cup third round clash against Oldham, who dumped them out of the competition at the same stage last year, when the visitors brought on 20-year-old midfielder Anton Rodgers, Brendan's son.
"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 was quoted as saying by British media.
"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."
Rodgers had shuffled his pack for the Oldham clash and left Luis Suarez, Philippe Coutinho and Lucas Leiva on the bench but all three came on in the second half as the visitors frustrated the seven-times winners in a flat opening period.
Iago Aspas broke the deadlock for the hosts in the 54th minute with his first for the club before Raheem Sterling's shot went in off James Tarkowski with eight minutes remaining to make the game safe.
The victory sent Liverpool through to the fourth round where they will face either second tier Bournemouth or fourth tier Burton Albion away at the end of January.
Meanwhile, Oldham return to a relegation scrap and have a home match against Stevenage Borough to look forward to on Saturday.
Their manager Lee Johnson said he also felt pride despite his side failing to match last year's 3-2 win at Boundary Park.
"We worked our socks off first half, we broke well and got ourselves into areas where we had shot," he said.
"We had corners, free-kicks ... so we certainly weren't just parking the bus. I thought our boys showed energy, particularly when we went 1-0 down. For a 20-minute period you may not have known who was the Premier League side."
The 32-year-old former Bristol City midfielder denied sentiment played a factor in the introduction of Anton Rodgers, an Ireland Under-19 international who has also played for Brighton and Hove Albion and Exeter City.
"He deserved it," Johnson said of the young midfielder who joined in July and has made 13 appearances this season.
"I didn't do it because it was Anton Rodgers, he's played in the Cup and the games before and he was magnificent in the game against Wolves (Wolverhampton Wanderers)- probably one of the best displays all season when we beat them 2-0 away.
"I wanted to go with a group that deserved to play at Anfield, he certainly deserved his minutes."
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