Mathias Doumbe missed a golden chance late on and Northampton had a penalty appeal turned down when Roy O'Donovan went down inside the box.
"After a very fiery first 15 minutes when Bury had a real go at us, we got ourselves together," he said.
"After that period, we limited them and I thought we had the better chances and were the better team.
"This keeps our little run going. It's another draw away from home at a difficult place and if that chance late on had fallen to McLeod or Platt rather than Doumbe we would have scored.
"We showed character and one thing I won't accept is when people say 'your team didn't put up a fight' because we always put up a fight."
Boothroyd was particularly angered by the decision to award Bury a penalty and deny O'Donovan's late appeal.
The former Watford boss said: "I said to the referee, are you trying to get me sacked or trying to be player/manager or something?
"If the Bury penalty was a penalty, the challenge on Roy O'Donovan was a penalty too.
"What I won't do though is make excuses. We're in there fighting and although we haven't got a win, the league's tightened up down there."
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- Chris Hackett
- Mathias Doumbe
- Ricky Ravenhill