The Welsh club eliminated United at Old Trafford on Saturday courtesy of Wilfried Bony's last-gasp header, after Fabio had been sent off for a reckless lunge.
Michael Laudrup's side could face Birmingham City, Bristol Rovers or Crawley Town in the fourth round, while they also face a UEFA Europa League round-of-32 meeting with Napoli in February.
But Tremmel is not concentrating on cup competitions, despite their momentous League Cup triumph last season, although he hopes their success will serve to boost confidence for Swansea's Premier League campaign.
They currently sit 13th in the English top flight, while the added work-load has resulted in injuries to key players, including Michel Vorm, Ashley Williams and Michu.
Tremmel said: "We've shown that we play against these big teams, they are just not sitting back and defending.
"If they want to play that suits us because we want to play as well.
"Last season we saw what a cup run meant but winning at Old Trafford can give you a confidence boost.
"We are still in the Europa League but we need some points in the Premier League.
"That's more important to us but every good result is good for confidence and we have to take the momentum from this, and win or draw on Saturday."
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