Having reduced the arrears against Chelsea to 2-1, substitute Carroll saw his headed effort pushed onto the bar by Petr Cech before the ball bounced down on the line.
Replays appear to show that the whole ball did not cross the line, a verdict that Carroll has refused to accept.
"I thought it was over the line," he told BBC Sport. "I thought it hit the other side of the bar which means it's in."
Liverpool went on to lose the match 2-1.