The 30-year-old lasted 17 minutes in the first-half and was replaced by Josh Onomah, who cancelled out Romaine Sawyers' opener for the hosts by the half-hour mark.
Brentford took the lead once again after Villa succumbed to their pressure in second-half.
Lasse Vibe pounced on a poor clearance from a corner-kick and sent his strike beyond the goalkeeper.
Villa pushed men forward in a bid to salvage a point but they were unable to find a breach in Brentford's defence.
"It was a tough night – really, really tough. We just didn't do enough. We simply didn't do enough with or without the ball," Bruce told the club's website.
"With our club, there's an expectation. That's why the cameras are here and we have to hit a certain level of performance.
"There's no timescales yet [on Albert Adomah's injury]. All we know is that he's got a knock to his hip. We're not sure how long it's going to be but he may be out for some time," he added.