Allardyce upbeat despite defeat
The home side enjoyed a surprisingly comfortable afternoon in a meeting of first versus fourth at Stamford Bridge, John Terry and Diego Costa earning the points.
Yet having done little before Chelsea's second goal, West Ham threatened a late rally when creating a series of chances - the best of which saw Morgan Amalfitano rattle the woodwork.
That charge at least offered cause for optimism for Allardyce, who praised his side's commitment.
He told Sky Sports: "After 2-0, there was an opportunity for a smash-and-grab job. But because one never went in, we have ended up disappointed.
"At least we created some good chances late on and didn't give up. We went right to the very end.
"I am not saying we deserved anything - Chelsea were the better team - but when you create the chances we did in the last 20 minutes, you want to stick one in and see if there are any nerves."
Even so, Allardyce was full of admiration for Jose Mourinho's side.
He added: "It was a combination of a top-quality team playing against us when we weren't on our game.
"I said if we were going to get anything, we would have to play our best - and even then it might not have been enough."