Lee Tomlin and Dwight Gayle put Posh 2-0 up within six minutes before two Keith Andrews spot-kicks, either side of George Thorne's strike, hauled Bolton back into the game at 3-2.
The home side were three goals clear once Mark Little and then Gaby Zakuani struck before Benik Afobe and Martin Petrov set up a tense finish.
"I'm obviously very disappointed with the result," Freedman said.
"We knew that individual mistakes could well influence a game played in very testing conditions and that is an area in which we let ourselves down.
"We weren't in the game for the opening 20 minutes and full credit to Peterborough for the way they started.
"But we were much-improved in the second half and it was pleasing to see the players continue to show such desire even when it looked as though the match had gone."