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Carey's penalty in the second period of extra-time sealed a 1-0 win at Newport County in a dour second round replay.
"We're going to go there and try and get a result," 27-year-old Carey said.
"No-one will give us a shot at getting a result, but we've showed we can battle as a team and it's the FA Cup so you never know."
The win meant the Pilgrims, who were beaten in last season's League two play-off final, reached the third round of the FA Cup for just the second time since 2010.
"My whole family are mainly Liverpool fans, so I'm sure some of them will make the trip over," added the Irishman, who is rated as one of Argyle's top players, having scored 10 goals in 27 games this season.
"It's a great win for the club and as a team we stuck together and dug it out.
"We're getting stronger and harder to beat, we had our bad patch, but hopefully we can go on a run now because we're full of confidence and we've started to learn how to grind games out.
"The main aim this season is to get promoted - we can enjoy that day (at Liverpool) when it comes - but first of all we need to go back to the league and rack up more points and that's what we'll do, but the FA Cup won't be a distraction whatsoever."
Argyle striker Ryan Donaldson will miss the tie at Anfield with a broken jaw.
The 25-year-old was injured in an accidental clash in training ahead of the Newport replay.
"It's really disappointing for him as he'd got himself into the side," boss Derek Adams said.
Fellow forward Jimmy Spencer is also on the sidelines after he broke his ankle in a training ground slip.
Liverpool-supporting Plymouth Argyle midfielder Graham Carey hopes they can cause an FA Cup upset when they visit Anfield in round three.