Jack Harrison's late goal sealed all three points for the Whites, on a day which threatened to turn out differently.
Burnley's loss at home to Newcastle United meant Harrison's goal ultimately proved immaterial, but Leeds nerves were jangling throughout the 90 minutes as the Clarets went into this round of fixtures in the driving seat.
Brentford were left with nine men following an injury to Kristoffer Ajer during the second half, before Sergi Canos was shown two yellow cards and sent for an early bath.
"You can see in our dressing room after the game they were very disappointed and very angry. It just shows how much the game meant," Frank said in his post-match press conference.
"You can just see we were building momentum, it would have been long 20 minutes for Leeds, that's for sure. And then we need to play 10 against 11."
Frank congratulated Leeds on their successful survival bid, but was left disappointed by his side's final day performance.