Carroll made a successful return from a nine-week injury lay-off on Saturday, heading the Hammers to a much-needed 1-0 win over Swansea at Upton Park.
"The points had dried up a bit so the lads are delighted with the win today," Carroll told West Ham TV after the match.
"You could see when I scored everyone was celebrating. And everyone was sliding in with last-ditch tackles at the end. We needed the three points.
"It was good for us to get the win. It will be good for all the lads to get a rest in a rest now and hopefully we can get three points at the end of it."
Hammers boss Sam Allardyce was full of praise for Carroll following his typically bruising display against the Swans.
He proved to be the perfect foil for Kevin Nolan, offering the forward two good goalscoring opportunities with knock-downs from long balls.
Allardyce had been reluctant to start Carroll after such a long lay-off, but the striker had no qualms about playing the whole 90 minutes.
"I've had eight weeks off and I've been working hard in the gym so my fitness is still high," he added.
"All the physios and backroom staff have been helping a lot to keep me fit in the gym when I couldn't run. Obviously it showed with getting 90 minutes. It felt good. We got three points and I got the goal, so it was great."