Despite coming away without a share of the spoils, Carroll believes that the Hammers should be happy with their performance against the title challengers.
"We put in a good effort and were hard done by with the two penalties we gave away and losing the game to that," he told the club's official website.
"But we put ourselves about and were in the game all the way to the end. We did great and I think we could have got the three points or a draw - it was just disappointing that the decisions were made for the two penalties."
West Ham are back in action on April 15 when they travel to Arsenal in the Premier League.