Kevin Schade struck a hat-trick as the Bees dominated on the day.
Andrews said afterwards: "I'm really pleased because Bournemouth can be a very difficult opponent. I recently watched the two games from last season back and they were very difficult.
"The matches they've played recently... their performances haven't given them the results they've maybe deserved. We're very respectful of the individuals and the capabilities that they have.
"So, to play the way that we did, particularly in the first half, to control the game, was impressive."
Asked if he was comfortable with their defending, the Bees boss added: "Not entirely! But it's not always down to you, obviously. It's down to them and the bodies they threw forward.
"The momentum built against us isn't always easy to deal with, but we got the fourth goal and it made it a bit more comfortable for the last 60 seconds. It was never going to be easy against them today."