West Brom boss Darren Moore refused to blame his misfiring Baggies after Lewis MacLeod's injury-time header denied Albion victory.
Brentford snatched a 1-1 draw at the end after Harvey Barnes' 77th minute strike looked to have given the hosts the win.
Jay Rodriguez missed an early open goal while Hal Robson-Kanu headed wide and Matt Phillips hit the bar after Brentford survived a first-half battering at The Hawthorns.
The point still lifted Albion up to third in the Sky Bet Championship, five points behind leaders Norwich.
West Brom are the highest scorers in the division with 42 goals and Moore cut his side some slack after Monday's match.
He said: "You've all seen the game, I'm pleased with the performance – it was a dominant display – but the goal we conceded, you're never too happy.
"Right from the second minute, when Jay missed his chance, we were trying to go out and win the game.
"We could have been bit more ruthless but I can't complain because the boys have been showing that. As long as we create, be inventive and get performances we'll win more than we'll lose.
"The analyst guys said we had 23 chances and 34 crosses, because of the way the team has been in recent weeks you'd think it was a win but that's football and it's never like that."
Barnes struck 13 minutes from time when he scored his eighth goal of the season, firing in high after Chris Mepham blocked his first effort.
But MacLeod, on as a 83rd minute substitute, headed in Emiliano's cross in the first minute of stoppage time to level.
It was Thomas Frank's first away point as Brentford boss, with the Bees having lost six of their previous seven games under him.
They climbed to 17th, four points above the relegation zone, but Frank insisted Albion's goal should not have stood after Dwight Gayle pushed Ezri Konsa in the build-up.
He said: "I think it's a push. It's one of those, we see a lot of small mistakes from players all over the pitch, also sometimes from the referees. It happens, everyone tries to do their best – but we came back.
"We talked before the game about needing to leave everything out there. The boys did well in that aspect, everyone could see in the first half we were hanging in there.
"It's not how we wanted to play but we were playing against the best home side in the division."
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