The non-leaguers pushed Brentford all the way on Monday before succumbing 1-0.
Rooney, afterwards, confirmed Andrews visited the home dressing room to speak to the Macclesfield players.
He stated: "He came in and said a few nice things about us. The lads have been outstanding and I couldn't be any prouder of them.
"That little bit between, the lads have been incredible. To lose 1-0 to a Premier League side to an own goal, I couldn't have asked more of them. Our season doesn't stop tonight, we get back to our bread and butter and bounce back Saturday."
Macclesfield striker Danny Elliott also said: "Keith Andrews came into our dressing room and told us he was relieved and paid a lot of respect to us.
“For a Premier League manager to do that is nice. It shows the gap isn't necessarily massive. We should be so proud of ourselves. The run highlights the club nationally and it's nice that a Premier League manager was pretty scared of us!”
