Nick Barmby admitted his Hull City side were fortunate after Robert Koren's strike halted their three-match losing streak.
Koren scored with a delightful half-volley to give the Tigers the lead three minutes shy of the half-hour mark despite Peterbrough's dominance.
Posh will feel aggrieved that they were not awarded a penalty when Hull 'keeper Vito Mannone looked to have brought down Daniel Kearns, as Barmby's side managed to end the visitors' five-match unbeaten run.
"We rode our luck in the first half hour and maybe they should have had a penalty," Barmby, who was this week appointed as full-time manager after a temporary stint, said.
"If it had happened to us we would have been disappointed not to get a penalty. But we have had a few penalty shouts go against us recently, so maybe it evened itself out today.
"Then in the second half I thought the shape of the team was a lot better.
"All credit to the lads as they worked it out what they should be doing and we showed what we can do. We could have scored a lot more goals and we did.
"Peterborough are no mugs and to nil a team like that is an achievement."
Barmby also praised Koren, who hobbled off in the second half with a dead leg.
"He's scored quite a few from outside the box this season," Barmby said.
"We are fortunate to have Robert Koren in our side, and it was a great goal, but I thought everyone was fantastic.
"We created a lot of chances in the second half and the work rate and commitment of the players was tremendous."
Peterborough manager Darren Ferguson was left bemused by the failure of referee Andrew Madley not to award a spot-kick.
"The penalty incident is such a bad decision," Ferguson said.
"When we asked the referee at half-time why he didn't give it, he said that the goalkeeper made an attempt to win the ball but didn't win it. So he was basically saying it was a penalty.
"The boy (Kearns) has got a six-inch gash in his leg. But what can you do?
"However, we were excellent and that is the best we have played for a while. We should have got a result out of the game.
"Emile (Sinclair) had two great chances early on and did everything right. He was just unlucky.
"We were far more fluid in the first half, but we didn't test their goalkeeper enough in the second half.
"I'm happy with the performance as a whole though and there are a lot of positives to take from the game."