The Tigers took a first half lead thanks to a neat finish from Jake Livermore but were denied all three points by a late Matej Vydra equaliser
The visitors were looking for only their second away win of the Premier League season and appeared to be on their way when Jake Livermore gave them the lead just before the half-hour mark.
Hull were prevented from doubling their lead as Ben Foster pulled off a double save in the second half to keep out efforts from Tom Huddlestone and Ahmed Elmohamady.
And Foster's heroics would prove crucial when Matej Vydra scored the equaliser four minutes from time, leaving Bruce to bemoan what might have been.
"It feels in the dressing room afterwards like we have lost the game," he said.
"I can't remember my goalkeeper making a save in the second half. We frustrated West Brom and counter-attacked them and Jake Livermore took his goal well.
"We had the best chance to seal it and at 2-0 we would have put the game to bed but Ben Foster has made a great double save."
Hull sit 12th in the Premier League on 20 points and, despite his disappointment with the result at The Hawthorns, Bruce is satisfied with the progress Hull have made.
"Maybe I'm nit-picking but we're frustrated and disappointed. Before the game we probably would have taken a point.," he added.
"We're on 20 points at Christmas so we're bang on schedule."