Mike Grella's goal ensured the Shakers moved nine points clear of the relegation zone with just three games left to play.
Bury had looked doomed after going 13 games without a win but have now won three of their last four.
"We're as close as we can be to survival," said Barker. "Wycombe would need to win their three and we'd have to lose our three, which is possible I dare say.
"I thought we were excellent for the first 20 minutes but then went away from what we're good at and didn't really get going in the second half.
"But what I will say is I've asked the players to win games ugly, to dig in and show some guts and determination, and that's what they did."
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