The Bees were made to fight all the way after Robbie Simpson's 10th-minute opener was cancelled out by Daggers' Romain Vincelot, but Gary Alexander headed home substitute Nicky Forster's 87th-minute cross to lift Scott's side up to ninth place.
Still said: "I was very disappointed because we showed tremendous discipline for the whole game apart from a few minutes at the end and that has cost us.
"I'm doubly disappointed because I thought we created some fantastic opportunities and I didn't see this as a game we should have drawn - I think we could have been worthy winners.
"We were very strong and disciplined apart from those couple of minutes but we are a very young side and I hope they learn from that.
"Brentford didn't play anywhere near the level they are capable of but they won the game and that has to be a lesson for us."
Source: PA
Source: PA