The Bees came from behind to win 3-1, with Igor Thiago scoring twice on the day.
"It was thoroughly deserved, it was an outstanding performance," Andrews said.
"We maybe edged the first half without creating too many clear-cut opportunities - I would say we looked the more likely.
"Half-time, going a goal down, I just wanted us to remain calm and focus on what we talked about before the game.
"There were a couple of tweaks on how we could improve things... I thought we were outstanding in the second half, and our performance levels went through the roof."
Kevin Schade also struck for Brentford and said afterwards: "It was a tough first half, but a good second half. In the end, I think the win was deserved.
"We just had to get the basics right after half-time. They played much better at the start because we were playing so badly!
"We didn't change any structure or tactics, we just had to get those basics right."
On his goal, he added: "It was a throw-in and I just made sure I got the second ball, and headed it!"