Defender Mark Connolly was sent off for a professional foul after just 50 seconds before goals from Sam Saunders and Clayton Donaldson put the Bees 2-0 up at the break.
Nicky Adams pulled a goal back for the home side with a stunning 30-yard drive but Barker was over the moon with his battling side.
He said: "The players reached another level with this performance. To battle for what was nearly 100 minutes with 10 men was absolutely fantastic.
"There are miles more positives than negatives. Our attitude and desire were absolutely fantastic."
Barker admitted that he had never witnessed such a quick sending off as a player or manager.
He added: "It was a great effort after that. To achieve what we did in the second half with our togetherness and determination was brilliant."
Barker felt Brentford defender Harlee Dean should have received a straight red card from referee Lee Collins shortly before the interval for lashing out at striker Jamie Proctor.
The Crawley boss added: "The centre-half clearly raised his arm and it was a clear sending off. Proctor went on to play superbly when you bear in mind he was on his own through the middle for 100 minutes.
"We've had three excellent performances in eight days, winning one, losing one and drawing one and we have deserved more. Unfortunately we are rapidly running out of players."