Kevin Schade was sent off just minutes before Dango Ouattara hit his first-half winner at Villa Park.
Andrews said afterwards: "In the first half, we could’ve created more with what we had and the positions we got into, and then, ironically, when we went down to 10 men is when we scored," said the Bees' head coach.
"There was a calmness in the way we defended deep for large parts of the second half. There was confidence in each other.
"Whoever was on the pitch at any moment was so impressive. It was a performance that typified us."
Bees defender Kristoffer Ajer also said: "Just incredible.
"That performance really sums up what we are as a club.
"The staff and players work so hard every day to prove everyone wrong and to develop individually but also as a team.
"We worked so hard defensively for so long and we saw that when it clicks, it really clicks. That was the ultimate Brentford performance."