Rodgers senior, whose side lost 3-2 at Boundary Park last season to exit this competition at the fourth-round stage, was so concerned that the football gods would write the perfect script that he had told his players in the build-up to the Anfield clash that they needed to be extra wary of "their number 17".
As it turned out, Anton only entered the fray seven minutes from time and with Liverpool leading at that point, after Iago Aspas had opened his Reds account and James Tarkowski had scored an unfortunate own goal, his father was able to savour the sight of his son running on to cheers and applause from the Kop.
"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 after Liverpool's 2-0 win.
"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."
Such admiration may not be have so forthcoming had the Liverpool boss not turned to his own substitutes at half-time, though.
After an uninspiring first 45 minutes, Lucas Leiva and Philippe Coutinho were both called upon to rally the troops and the Reds soon took control with Aspas hooking home a half volley nine minutes into the second half.
Even then their League One opponents failed to cave in. Oldham, who thought they should have had a penalty when debutant Gary Harkins was shoved to the turf by Jordan Henderson, went close through Michael Petrasso and it needed the introduction of Luis Suarez and a second goal, which came courtesy of the otherwise-brilliant Tarkowski following Raheem Sterling's effort.
Oldham boss Lee Johnson saw the fact Liverpool needed to introduce a trio of star names as a testament to how well his team were playing.
Rodgers explained: "We needed to have more speed in our game and a bit more intensity. You don't want to do it (making the substitutions) but the last thing I wanted was the game to go to a replay.
"I think you learn as a manager. As you get more experiences you can either wait for it to happen or, if you don't think it's going to happen, you have to change the momentum of the game by making your subs.
"Coutinho came on, Lucas came on and they add that bit of intensity and greater purpose to our play. That allowed us to get better control."
- Sports & Recreation
- James Tarkowski
- Iago Aspas