Palace missed a penalty, hit the woodwork and played the final 15 minutes with a man advantage, but ultimately failed to cancel out Manuel Lanzini's opener.
Pardew admitted that his side were second best in the first half, but believes that they did enough after the interval to warrant something from the game.
"I was disappointed with a lot of aspects of the game. We didn't start well and they got a deserved lead. We had to make change at half time because weren't playing with the fluidity as we have done. We were better in the second half," he told BBC Sport.
"We should have at least got a draw. With the penalty I was thinking with the week [Christian] Benteke has had it'll go in. That would have been a lifeline and would have turned the game on its head. We would have gone in 1-1 at half time.
"This happens in the course of the season. Adrian made a good save at the end. The Hammers for their faults... you couldn't fault them today defensively."
The defeat is Palace's first in their last five Premier League outings.