The 29-year-old came on as a substitute to score a very late equaliser at the London Stadium on Monday, in his first outing for the club so far this year.
Carroll said after the match: ''I thought we played well throughout. We took points off them, and it's a point for us, so it was a good result in the end.''
He added: ''We've still got five games left and we've got to win them as no one is safe. It's tough at the minute and we've just got to keep working.''
West Ham ensured that Stoke remain firmly in the drop zone, with four games to play before the end of the season, but 'Potters' manager Paul Lambert doesn't believe they are a lost cause.
He said: ''We are still in the fight. It's not as if we are on the ropes and hanging on. The point could be huge for us and we still have to win three games.''
Lambert cautioned: ''There are a lot of hard fixtures for a lot of teams at the bottom so it will be interesting. It won't be for the faint-hearted.''