The Baggies opened a surprising lead at London Stadium before Andy Carroll's second-half double, including the winner in stoppage time, completed the Hammers comeback.
It was Albion's second game in three days, and Pardew believes this caused his side to run out of energy by the end of the game.
He told Sky Sports: "The two day turnaround has cost us in the end and we ran out of legs and could not keep going. It was heart-breaking for the players. It is such a disappointment to concede a goal like that.
"We were better in the first half, but we conceded too much possession in the second half and the turnaround has done for us.
"We were unfortunate to lose Matty Phillips in the warm up. We had players hanging at the end. I tried to freshen things up, but it was difficult and they had more energy than us and it showed."