Headers from Marcus Tudgay either side of half-time gave Wednesday a comfortable-looking lead but the visitors reacted well and, after Jake Livermore reduced the deficit, came close on several occasions to nicking a point.
However, Peterborough failed to net the elusive equaliser and the former Kettering boss criticised his team for giving too little, too late.
"We've prepared as if it was the World Cup final this week," he said. "I drove to Blackpool and watched Sheffield on Tuesday, prepared for three days solid on how we were going to play.
"So, as staff, we did our part but the players let the club down.
"I've been sat here I don't know how many times after we've gone behind," he added. "Against Coventry we were down 2-0 and came back to 2-2. Cardiff we go 4-0 down and get back to 4-4.
"It seems we have to go behind before we start playing.
"Well, if you're 2-0 down it is easy to play because there is no pressure on you. But if it is at 0-0 that you've got to go and earn your corn.
"That's when it matters, and that's why we're struggling - because people don't have the bottle to go and do it when it is 0-0."
While the result prolonged the visitors' woes, it stretched the Owls' winning streak to three on the trot and propelled them five points clear of the Championship relegation zone.
However, Wednesday manager Alan Irvine admitted he had been concerned this form would hamper his side heading into the match.
"I hope [the momentum] is really valuable and I hope it keeps going," he said. "The danger, certainly today from my point of view, was that, having won at two very difficult places in Barnsley and Blackpool, everyone assumed we would win today.
"And obviously you can't go into any game in the Championship thinking in that way.
"I was really concerned about today's game in terms of how the players might approach it mentally and we've talked about that really since the final whistle at Blackpool through to the start of the game today.
"And I have to say they really took all of that on board and responded brilliantly.
"It's a great start but we still need an awful lot more wins and the moment we think that the job is done, then we will have problems again."