Ed Kennett top-scored with 12+1 for the Bees, who travel to Eastbourne on Monday knowing that a victory will give them a play-off place.
Bees Co-boss Peter Oakes said to his club's website: "It's disappointing, and it's becoming the story after almost every home match. We didn't have enough race winners and we had far too many last places.
"Those who are in the doldrums have to snap themselves out, it's as simple as that. You're always looking in any sport to see if you need to make changes, and there comes a time when you do - but equally, we know what this team is capable of.
"Over the last two meetings, the only rider who can come out with total credit is Ben Barker - for everyone else, the good and the bad has been spread around, and that's led to two ugly performances.
"Now we need to win on Monday. We can't rely on Peterborough losing their last two away matches, we've got to make sure we get the points, and we can do that - at the moment we seem to be a better team away than at home."
BUILDBASE BEES 43: Edward Kennett 12+1, Chris Harris 8+1, Ben Barker 7+1, Olly Allen 7, Ricky Wells 6+1, Rory Schlein 3, Joe Haines 0.
PETERBOROUGH 47: Troy Batchelor 13, Niels-Kristian Iversen 11, Darcy Ward 8+1, Claus Vissing 7+4, Mads Korneliussen 7, Henning Bager 1, Kenneth Hansen R/R.