Anton Forrester's strike was enough to win the battle between two of League Two's struggling sides in difficult conditions at Gigg Lane.
Bury jumped above their rivals into 20th place, two points clear of the relegation zone.
"It turned into a battle, which pleased me because we need to keep clean sheets," said Flitcroft.
"Before I came here there were four clean sheets but now we've had three in eight games and that's a pleasing stat for me.
"I talk quite a lot about the way I want the game to be played, moving the ball around the pitch, but the character and resilience they showed here was good.
"When you're building a project you've got to look at the short-term and the short-term priority was to bring in experience.
"When the muck and bullets are flying sometimes young players can go under but we have a very good spine and leaders out on the pitch.
"To play one-touch football on that pitch takes bravery and courage. The last 60 minutes became a battle and we had to dig in but I enjoyed the first 30 minutes.
"We've shown both sides of what we can do."
- Sports & Recreation