The Bees won courtesy of a Sam Heathcote own goal on 70 minutes and sees them face West Ham in the next round.
Andrews said afterwards: "It was a really tough test. We knew it would be. Macclesfield play with a real spirit and the way they approach the game they had confidence from the last round.
"First half I didn't think we did certain things well enough. I tweaked a couple of things at half-time but it was mainly the basics and I thought we did them a lot better in the second half.
"We eventually wore them down and got the goal we clearly needed. The pitch will never be used as an excuse but it was different I suppose. Different from what the players are used to training on and playing on daily - that's a fact.
"The fact we are a pretty likeable club and we are normally the underdog, but everybody wanted us to lose tonight and we had to deal with that."