The derby clash lived up to the hype and although Dale forward Ian Henderson was shown a second yellow card in the 44th minute, Bury struggled to break the visitors down.
Dale would have gone top of Sky Bet League Two with victory and still had chances of their own, but were pleased with a point after goalkeeper Josh Lillis made a stunning save in the closing stages.
"We had enough chances to win it so we're disappointed not to beat a very good Rochdale team," said Flitcroft.
"It's another clean sheet and I was expecting the net to ripple a couple of times at the end there. We got in a few times.
"We saw the other side of Rochdale. We know they're a good footballing side, but they were resilient second half.
"They still carried a threat and were difficult to break down, we just lacked that ruthless edge.
"Josh Lillis did well, but that's the next part of the challenge for us - to take those chances and beat the top teams."
Dale lost top scorer Scott Hogan to an early knee injury but had the better of the first half as Jamie Allen and Henderson headed over.
Bury replied with Danny Nardiello firing over and after being booked for handball, Henderson was sent off for pulling back Jake Carroll just before the break.
Bury's Pablo Mills clipped the bar after the restart, while Michael Rose and Peter Cavanagh fired inches wide for Dale.
Lillis then denied Tom Soares and Nardiello before tipping over Carroll's last-gasp header.
- Sports & Recreation
- Ian Henderson
- Josh Lillis