The Hammers were beaten 3-2, with a James Collins own goal 11 minutes from time sealing victory for the visitors.
But Allardyce said: "We have got to take it on the chin and I think we did the best we could and played as well as we could and we are disappointed that we haven't got anything from it.
"It is disappointing to lose, but it is even more disappointing when your most creative player (Mohamed Diame) leaves the field with what looks like a serious injury.
"The way we finished the last 30-35 minutes of the first half, unfortunately we didn't get to that tempo and that level of quality and started to sit a little too deep after the break.
"I thought we had seen that out and we were going to come good at the end like we normally do and maybe they would over-extend themselves and we could hit them on the break and get a third.
"To lose the second goal was a bit of a sickener for us but I thought 'see it out today lads and if it is not to be then let's get the draw and we move on'.
"But then to lose it to a freaky own goal is a little hard to take at the minute."