Accrington manager James Beattie was happy with a point which keeps them above 21st-placed Bury following their 0-0 draw.
Laurence Wilson was sent off in the 31st minute for Stanley but the Shakers could not get past their in-form Fulham loan keeper Marcus Bettinelli.
"I always ask my players to give 100 per cent and they did," said Beattie. "We defended as a unit and we were tremendous.
"We showed resolution, heart and desire and I am proud of the way we played for 60 minutes with 10 men.
"I thought Lawrie got the ball but the referee said it was a reckless challenge and two-footed. Lawrie said to me it was one-footed and it is something I will have to look at but it was a great response from us.
"We showed a lot of character and we are hard to beat. Marcus was top class and he is a top professional who has a big future in the game."