The former Liverpool striker, who scored a last-minute winner to cancel out Peter Crouch's opener for the Potters, said that he was happy to settle for a point after his team fell behind.
"It fell right into my path on my left foot, I swung a leg at it and it went in. I've trained for the last five days, I've been working with the physios a lot," Carroll told Sky Sports News.
"I had the second goal which could've been at the end, there's a shove at the back and that could be a penalty, if not then play on, but he didn't give it and we'll take a point.
"We've still got four games left, we've got to win them, no-one's safe, and we've got to keep working."
The draw leaves Stoke second from bottom in the table, five points from a position of safety, while the West Ham are seven points better off in 14th.