The Tigers were in the ascendancy throughout the first period and broke the deadlock on the half-hour mark when Jake Livermore completed a classic piece of counter-attacking play.
Managerless West Brom refused to lie down and came back after the break firing but Hull's organised defence appeared to be equal to the challenge.
The sting came late however when Matej Vydra found himself in space inside the Hull box before turning and firing home his first Premier League goal.
Bruce conceded the late strike hurt after his Hull side dominated possession throughout the afternoon, but were unable to close the game out and take the three points.
"For all the possession they had I can't really remember our goalkeeper making a save," he told Sky Sports.
"In the second half we arguably had the best chance to go 2-0 up but they nicked it. But they had a real bit of quality coming from the bench in [Matej] Vydra and he's got them a point today.
"We're disappointed because we were two or three minutes away from what would have been a huge victory for us.
"We have made huge strides in the last few months, we were in the Championship last year and a lot of the players are coming to terms with this level for the first time."
West Brom appeared rejuvenated after the break and threatened the Hull defence, but Bruce's back four - marshalled by captain Curtis Davies - remained organised and resilient.
However, Bruce understands that a game can be changed in a split second and was left ruing a momentary lapse in concentration.
"It is the tiny little margins. It was the only time [Shane] Long got in behind our defence and that small mistake cost us," he added.
"I thought we were excellent in defence all afternoon but that one lapse in concentration has cost us the game."
Hull's goal saw striker Danny Graham intelligently hold up play before sliding a precision ball through to Livermore, who made no mistake in slotting beyond Ben Foster.
Bruce praised the on-loan Tottenham midfielder, saying: "It is a great goal; all goals are at this level. Jake [Livermore] has done great for us, we have given him the licence to get forward and he relishes in it.
"Danny Graham held up the ball well and passed it through, Jake finished well and it's just a shame it wasn't the winner because on another day it could have been."
Despite being pleased with his side's performance throughout, Bruce confessed the feeling in the dressing room was one of defeat rather than achievement.
"When you get bitten in the final minute like that it feels like a defeat rather than a draw," he said.
Livermore's parent club Tottenham sacked manager Andre Villas-Boas last weekend but Bruce remains confident they will be able to retain the player's services despite the changes at White Hart Lane.
"At the end of the day he is Tottenham's player and there has been a lot of change there this week," Bruce added.
"All the signs are that they are happy with Jake being here and if we could make that a permanent move we would love to keep him."
With the Christmas period in full swing, the fixtures come thick and fast with defending champions Manchester United visiting the KC Stadium on Boxing Day but Bruce feels his side are competing well in their first season back in the Premier League.
"We have Manchester United coming up, the Premier League is unforgiving, it is the biggest and toughest league in the world," he explained.
"It is a hard, hard slog and we are making a hell of a fist of it, we came away with a draw today and before the game we would have taken that."