The target man is targeting an extended run in football's oldest cup competition.
West Ham haven't gone on an extended FA Cup run since the 2010/11 season, when they reached the sixth round (quarter-finals) and were knocked out by eventual finalists Stoke City.
Prior to that, the Upton Park outfit reached the final of the competition in 2006, when a famous Steven Gerrard strike secured a last-gasp draw for Liverpool before they beat the Hammers in the penalty shootout.
And Carroll is targeting another cup run this season as he feels there is nothing better for the club, while he believes this could be the year West Ham finally make their mark on the tournament once again.
“There’s nothing better than a cup run for everyone at West Ham and I feel this is the season where we could go a long way in it," the 26-year-old target man is quoted as saying by the Daily Mirror.
“There’s no reason we can’t. We’ve had a good run this season, so why can’t we carry that on in the FA Cup?
"All the lads are looking forward to the replay and hopefully getting through to the next round.”
West Ham led at Everton in the cup last week but were pegged back by a late Romelu Lukaku equaliser. Tomorrow, Carroll and co face Everton in the replay, although this clash takes place at Upton Park.