Goals from Palace new boys Tom Ince and Joe Ledley gave the home side a 2-0 lead at the break, but Thievy Bifouma pulled one back early in the second half and Albion were pressing for an equaliser with 20 minutes remaining.
But referee Chris Foy pointed to the spot when Foster was adjudged to have hauled down Marouane Chamakh as the Eagles striker attempted to round the Baggies keeper.
Television replays suggested that Foster made a clean challenge and got a touch on the ball, but the England international's protests were waved away before Chamakh slotted home the penalty to give Palace a comfortable buffer.
"I was in complete shock when he gave the penalty," Foster said.
"We have just got to suck it up and get on with it. It is irrelevant what we see in the replays. It is fine lines. If we had put our chances in the net it would have been 2-2 and you never know what could have happened.
"From a personal point of view, my opinion is that I didn't think I fouled the player.
"It makes no odds now what my opinion is because the decision has been made, but I thought I got the ball and it didn't deserve to be a penalty."
Resurgent Palace were 2-0 up inside 27 minutes, and Foster is aware his side cannot afford another slow start when Premier League leaders Chelsea visit The Hawthorns on Tuesday night.
"We can't let it get to the point when we are one or two goals down in a game and then finally make a push for the game - we need to go from the very first minute," he added.
"We have a very tough game against Chelsea on Tuesday and that is what we need to do. Our home form is pretty good. We had a tough match against Liverpool and showed what we could do.
"We have to remain positive and take the second-half performance into the Chelsea game."