The Bees won courtesy of a Sam Heathcote own goal on 70 minutes and sees them face West Ham in the next round.
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Collins said at the final whistle: "It doesn't matter who you are playing against, we need to get the job done. Macclesfield could beat anyone on any day.
"If we can top it off with a cup run, then that would be great. Our fans deserve it.
"Credit to Macclesfield. They made it extremely hard for us. They put up a great fight and they deserve credit for that."