With Carroll now back to full fitness, the Hammers have their tails up and are confident of securing their top-flight status over the next few weeks.
"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."