Tony Mowbray admitted his frustration at his side's inability to finish off a spirited Burnley outfit.
The Baggies found themselves behind after skipper Jonathan Greening was harshly adjudged to have tripped Robbie Black in the area with Graham Alexandra slotting home the resulting spot-kick.
Albion drew level thanks to a fantastic Robert Koren volley then took the lead after Kim Do-Heon's free-kick was deflected past returning stopper, Brian Jensen, to give the hosts a half-time lead.
After the restart the Baggies missed a number of chances with Roman Bednar hitting a post when an open goal gaped and a number of other opportunities wasted.
"I was disappointed with the first-half performance," Mowbray admitted.
"You've got to give Burnley a lot of credit because they're a good football team.
"They play the game in a manner I appreciate.
"Yet for us to get back into a leading position at half-time meant we should have had enough to go on and see the game off.
"To be fair, we had the opportunities early in the second half to do that and at 3-1 I think it would have been a long way back for them after their midweek disappointment.
"But Burnley always had something to chase.
"They did that in the last ten minutes.
"They pushed their full-backs on and went man-for-man.
"They got a goal and good luck to them.
"The bottom line is goals change games and, if you score the third goal, I don't think there is any way back for them."
The draw means Albion will face a replay at Turf Moor on Tuesday 3rd February (KO 7.45) with the Baggies boss hopeful their second FA Cup replay of the season will be as successful as the first - a 2-0 victory over Peterborough.
"We've got to do it again and we'll wait and see.
"We did the same in the last round and it was practically déjà vu with Burnley's equalising goal.
"Their cross came from our left-back area across the six-yard box and it was a goal.
"At this moment, it's hugely frustrating.
"Peterborough was frustrating and today is frustrating as well.
"But it's part and parcel of football and we'll get on with it."