The defence which had not conceded a goal this season leaked four in 20 minutes at London Road.
Town led 2-0 but things went downhill after an error from goalkeeper Alex Smithies on the stroke of the interval and Clark said: "We shot ourselves in the foot in the final few minutes of the first half.
"We knew that Peterborough would come out with the momentum in the second half and that we needed to get back to the good work of the first 37 minutes, but we didn't do that. I'm as flat as a pancake."
Full debutant Graham Carey delivered the corner from which Jordan Rhodes nodded Town ahead in the 22nd minute. Eleven minutes later, Celtic loan man Carey doubled the advantage with a fine free-kick.
Smithies's gaffe allowed George Boyd to halve Peterborough's arrears and they needed only five minutes of the second half to level through Aaron McLean.
The turnaround was soon completed with a goal claimed by Craig Mackail-Smith and a fourth from McLean after 67 minutes sealed Town's fate.
Town will need to sharpen up to have any hope of causing a Carling Cup shock against Everton on Wednesday.
Peterborough United: Lewis, Little, Langmead, Bennett, Ofori-Twumasi (Rowe 46); Davies, Wesolowski (Lee 84), McCann, Boyd; McLean (Hibbert 82), Mackail-Smith. Unused substitutes: Piergianni, Mendez-Laing, Tomlin, Collis.
Huddersfield Town: Smithies, Peltier, McCombe, Clarke, Carey (Roberts 61); Pilkington (Croft 69), Johnson, Gudjonsson, Arfield; Rhodes (Novak 65), Garner. Unused substitutes: Kay, Robinson, Bennett, Ridhalgh.
Referee: I Williamson (Berkshire).
Man of the match: Aaron McLean.
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