"Obviously we want to have the best cup run possible and we all have to be ready for that.
"Domestically, we've not had the easiest of seasons and I think this is a good chance for us to try to have a successful campaign.
"The FA Cup is such a historic trophy and I think trying to go as far as we can is obviously going to be the aim. Hopefully we can get the win."
Gomez's second-half outing against the Black Cats on Wednesday evening came as a result of the injury to Wataru Endo.
The Japan international is now facing 'quite a long time' out on the sidelines, according to Arne Slot.
"I'm gutted for Wata," Gomez continued. "He's such a treasured part of this squad and we appreciate him so much.
"Who he is as a person and how he plays, I think that showed in him trying to carry on.
"I think we all know that it's such a frustrating part of the game and we know how hard he'll work to come back stronger.
"Hopefully he comes back as soon as possible and has a chance to go to the World Cup."
The character displayed by Endo and the rest of his teammates saw Liverpool become the first team to win at the Stadium of Light in the league this season.
And the nature of the victory, secured with Virgil van Dijk's 61st-minute header, was particularly pleasing for Gomez.