A point gained in a scoreless draw with Morecambe in midweek dropped the Shakers to third place.
But Bury gained a point on League Two leaders Rochdale and can regain second place if they win their game in hand over Bournemouth.
And Bury boss Alan Knill wasn’t too disappointed his side didn't collect all three points.
He said: "I think any point at this stage of the season is a good one.
"It could have gone either way because they are a tough side. But the good thing is we have not lost.
"We just lacked that killer instinct round the box. And the last bit is the hardest bit."
Former Macclesfield and Stockport boss McIlroy said: "It was a great result and a great performance. Bury are a good side and the game could have gone either way.
"We had the better chances over the 90 minutes and limited them to only a few clear cut opportunities."
Bury had late chances to win the game through top scorer Ryan Lowe and skipper Stephen Dawson.
Both efforts failed to hit the target and that was the story from both teams.
Morecambe certainly didn’t come for the draw and carved out some noteworthy opportunities of their own.
Craig Stanley had a hat-trick of shots from the edge of the area while Mark Duffy went close in a second half distinctly better than the first.
However, the clean sheet was a pleasing one for Ryan Cresswell, starting a game for the first time since November 24, and he deputised superbly for the suspended Efe Sodje and Knill now has plenty of competition for places in most areas of the pitch.
And if Knill gets Andy Bishop firing on all cylinders then the Shakers could well make-up for last seasom’s play-off heartbreak.
Bury: Brown 7, Scott 6, Futcher 7, Cresswell 7, Newey 6, Dawson 6, Hewson 6 (82 Raachi), Barry-Murphy 6, Jones 6, Morrell 5 (66 Bishop), Lowe 7. Subs not used: Belford, Buchanan, Baker, Elliott.
The Shakers had moved up to second place on Friday night when they bounced back from defeat at Chesterfield with a 1-0 home win over promotion contenders Shrewsbury.
The match winner was top scorer Ryan Lowe, pictured, who coolly dispatched a late penalty after skipper Stephen Dawson was brought down. It was Lowe’s 13th goal of the season.
The win delighted Knill and handed the Shakers control of their own destiny in the promotion race with matches to come against Rotherham and Notts County – the only teams who can push them out of an automatic promotion slot if they win their games in hand.
Knill said after the win: "It is pretty intense for the players at the minute with games and training. We are on a good run and hope to get a few more points and then we will be able to give them a bit of a rest.
"At the moment they are doing fantastic and they are an absolute credit to the football club.
"I have been delighted by the players and we are a better team this season. We have more in our armoury and there is more movement and energy. I hope it continues.
"We were fantastic. From the start to the finish we were excellent and considering that it was third against fifth, it was very one-sided.
"We just looked sharper and quicker and pressed the ball better and I was so pleased with that. But the most pleasing thing was the end result and the three points."
Bury's crowd had 1,200 more supporters in the home section than for the last home game against Macclesfield.
And it is estimated more than 500 of those were other club’s supporters who took advantage of the entry for £5 offer on display of their season tickets.
The initiative was discussed at Bury’s board meeting this week and the success of the scheme may encourage the club to run it again.
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