Baggies boss Roy Hodgson was again left feeling robbed after watching Albion dominate for long periods but lose for a seventh time on home turf.
Counter-attacking goals from Andrew Surman and Steve Morison saw Norwich win 2-1 and steal three points after being on the back foot for long periods.
Albion started well and were denied by John Ruddy and the woodwork as the visitors took the lead against the run of play minutes before half time when Surman volleyed home.
But after Shane Long had levelled from the spot, Albion were again undone on the counter as they pushed forward in search of a winner. Steve Morison this time heading Norwich into the lead with just ten minutes remaining.
The Baggies searched again in search of an equaliser but were unable to prevent another frustrating result in front of home support.
"All defeats are painful, especially the ones here," said the Baggies boss.
"Wigan was a very similar situation where we lost the game to two counter-attacks after such a lot of chances and possession.
"It was the same again today.
"I didn't think we played very well in the first half.
"We had a little spell before half-time when we actually played better and started playing the type of football we are capable of playing.
"And, amazingly enough, it was in that spell they scored their goal.
"In the second half, we showed a lot more energy and endeavour and when we equalised I thought it was just reward for the effort we made.
"We plugged away and plugged away and got it.
"Then we got mugged again on another counter-attack.
"Norwich were able to hang on for a victory that I'm sure their manager felt they deserved through their organisation and determination.
"But, for us, this defeat feels a bit harsh.
"We had a couple cleared off the line and their keeper made a few good saves.
"Our goalkeeper, quite frankly, wasn't really involved if you don't include his long kick-outs.
"But that's football. We've got to get over it and deal with it.
"We need to try and get back to winning ways and in particular get back to winning ways at The Hawthorns because it must be very frustrating for the fans that come and see us losing at home so regularly."
Can Albion find a return to winning ways at The Hawthorns? Have your say here at Baggies Banter.