The hosts looked set for a fifth win in six after first-half goals by David Worrall and Ryan Lowe. But Courtney Herbert pulled one back in the 66th minute and substitute Adebayo Akinfenwa headed home with 16 minutes left to stretch the Cobblers' unbeaten run to four.
"I'm pleased with a point because it was a fantastic comeback but I'm very disappointed with the way we played in the first half," said Sampson.
"We just didn't get out of the traps and we can't keep letting teams have a two-goal start on us.
"I'm delighted with the comeback - at the moment they don't know when they're beat - but it'd be nice to go in at half-time with a 2-0 lead rather than a 2-0 deficit.
"Bury got in their stride and I thought our keeper Chris Dunn was man of the match because he pulled off some great saves."