The Merseyside outfit secured their ninth win on the bounce with a 2-1 victory against the Hammers on Sunday.
The result has moved the Reds back to the top of the league table, two points ahead of Chelsea and four over Manchester City, who have two games in hand.
After the match at Upton Park, Carroll wrote on Twitter that West Ham were "unlucky" not to come away with something against "this season's champions".
We were unlucky not to get something today against this seasons champions 🏆— Andy Carroll (@AndyTCarroll) April 6, 2014
Carroll signed for the Hammers last summer for a reported £15m following his £35m switch to Liverpool from Newcastle United back in January 2011.