Carroll's 77th-minute header was the first time he had scored at Upton Park and he revealed he was delighted to be off the mark in front of the Hammers' supporters.
"It's a great feeling to score anywhere, but when you've got the fans behind you like this, singing your name after you've scored, it's even better," he said.
"Coming off the pitch, man of the match and with three points, it's a great feeling. The fans are great, they got behind us and they were like the 12th man, helping us along.
"Even when Swansea put the pressure on late in the game, they gave us confidence with the singing and cheering us on. It's great."