Aspas, a summer signing from Celta Vigo, finally broke his Reds duck at the 11th time of asking with a hooked half-volley in a 2-0 third-round win over Oldham at Anfield as Rodgers entrusted his fringe players with righting the wrongs of last year's loss at Boundary Park.
However, it was far from plain sailing for the hosts and Lucas Leiva, Philippe Coutinho and 20-goal forward Luis Suarez were all summoned from the substitutes' bench to seal their progress, which was confirmed thanks to James Tarkowski's late own goal.
"They have to contribute - I can't rely on 11, 12 players," said the Liverpool manager.
"(Goalkeeper) Brad Jones coming in was excellent, Brad's been a really loyal number two. He didn't have much to do, but what he did do with his hands was clean and his distribution was very good.
"Iago - it's important for his confidence. It's been difficult when you have a world-class striker playing week in, week out and getting goals. Then you've got Daniel Sturridge supporting, so he's been the cover player a lot of this season apart form the opening period.
"It was good for him to get his goal in front of the Kop and hopefully that'll give him a little bit of confidence."
Perhaps mindful of last season's exit at the hands of the same opponent, Rodgers called for the cavalry at half-time by introducing Lucas and Coutinho, while Suarez's late cameo was a sign his plan A did not quite materalise.
Rodgers added: "You hope in a game like this to rest a number of players.
"Obviously Lucas and Coutinho have played all of the Christmas period, hard games, so the ideal scenario would have been to let them recover. But we also wanted to win the game, we didn't want a replay. Second half we were more lively in our game and ended up with a good victory."