Keane Lewis-Potter and Mathias Jensen scored the goals for the Bees at Hillsborough.
“We’re very respectful of the competition and the opposition," Andrews explained.
“I’m a big fan of cup competitions, so I wanted to treat it really seriously. Our players will always have the right attitude going into games – they won’t underestimate any challenge.
“We dealt with it well today.”
Youngster Romelle Donovan made his first start for Brentford and impressed his manager.
“He’s been champing at the bit, as everybody knows," Andrews said.
“He plays with so much enthusiasm; he wants the ball, he wants to be positive. I want our attacking players to try and make things happen, and I think he does that.
“He’s constantly learning the game, of course. He’s young and raw in certain aspects, and we need to keep nudging him in the right direction, but he was really good today.”