The Hammers are just one win away from Wembley, after drawing 1-1 with Manchester United at Old Trafford yesterday.
The replay of that fixture adds another game to West Ham’s hectic schedule, and could serve as a distraction as they chase a Champions League qualification spot.
However, Carroll insists that the squad are not prioritising either competition, as they want to be successful on all fronts this term.
"We want to finish in the top four and to win the FA Cup, definitely,” the striker said. “It’s the way the lads are and the manager is. We are not going to play a weaker squad for one and stronger for the other. We are going to go all out for both.
"If we can get past Manchester United and get into the semi-final, we have a real chance to win the FA Cup this year. We are still in with a real shout. We all fancy our chances against United at home.”
West Ham have named strong line-ups in every one of their FA Cup matches to date, but they are really closing in on the top four now.
The Hammers are in fifth place as things stand, and they are hot on the heels of both Manchester City and Arsenal.
West Ham have been in better form than both City and Arsenal in recent weeks and they still have Arsene Wenger’s side to play before the end of the season.
Hammers boss Slaven Bilic has previously stated that he would rather win the FA Cup than qualify for the Champions League, but with the prospect of European football so tantalisingly close it remains to be seen whether his attitude will change.