The Hammers were second best throughout and went down to goals from Frank Lampard and Eden Hazard, but they did have the ball in Chelsea's net, but Carroll's strike was chalked off for a push in the back on David Luiz.
Allardyce said: "Technically it was a foul, but I can show you about four of them outside the box he (referee Michael Oliver) didn't give.
"It was a brilliant dive by David Luiz and I think that bought him the foul.
"We were always in the game if we could score, but this year away from home scoring has been a massive problem for us.
"We had enough opportunities to score at least one."
Allardyce praised Chelsea and Lampard.
"Sometimes you can't defend against the quality they've got," he said.
- Sports & Recreation
- Frank Lampard
- David Luiz