The Bees won via goals from Dango Ouattara, Kevin Schade and Igor Thiago on the night.
Afterwards, Andrews said: “I’m very proud of everybody.
“There was something in the air; I felt good coming into the game.
“But you’re playing the Premier League champions, so it was always going to be a difficult evening. The way we approached the game was fearless.”
Meanwhile, Brentford's former Liverpool defender Sepp van den Berg also said: "I’m very happy, and I think we deserved it.
“We struggled a bit at the start of the game - the way they pressed and the way they built up was a bit different to what we expected.
“We stuck together very well, scored two good goals, and then the 2-1 was a bit frustrating; we have to do better there.
“But second half, coming out, the pressure we gave, the confidence we had the whole game, I’m just so proud of the boys.”