Andrews visited the home dressing room to speak to the Macclesfield players following the Bees win.
He told talkSPORT: "I have a lot of respect for what they've achieved and the journey they've been on.
"I love the English football pyramid, I've said this pretty consistently, I've played in a lot of it, I've coached in a lot of it.
"And I love what it stands for and the structure of it, and there's always journeys that clubs are on, and this club are on a really good journey.
"I think they've got a lot of spirit, a lot of character and a lot of talent. I just told them you gave us a real test tonight and we were concerned if we could get through it.
"I like stories like that, it actually fills my heart, so I thought they were immense tonight. I thought they were absolutely immense right to the end.
"They gave us a proper, proper cup tie that most people would have really enjoyed. I can't say I did, but again, a lot of respect for who they are and what they stand for."