But it was Hereford that will feel the more aggrieved at missing out on the win after a string of fine saves from Posh keeper Mark Tyler kept the visitors in the game.
Hereford made three changes from the weekend's FA Cup tie while Peterborough were unchanged from their fine win at Tranmere Rovers on Saturday.
It was Hereford that had the best early opening through the returning Stuart Fleetwood who found himself in the clear but shot too close to Tyler and the goalkeeper turned the shot away for a corner.
Then Peterborough were lucky to survive when Ben Futcher sliced an excellent cross from Alex Jeannin over his own bar five minutes later.
The main Posh threat was coming from the long throws of Jude Stirling which propelled the ball vast distances into the danger areas.
Other than that, the visitors were confined to long-range shots with Dean Holden, twice, and Richard Butcher shooting high and wide.
Hereford went close again in the 37th minute when Fleetwood's break played in John Eustace whose low drive was well saved by Tyler.
Fleetwood was at the heart of the action again five minutes into the second period when he spurned a great chance to open the scoring. Good work by Rob Purdie and Alan Connell set him up with a chance 10 yards out but he snatched at his volley and sent the ball wide.
Connell and Purdie were involved again when the next clear opening arrived. This time it was Eustace who benefited from the build-up to drive in a low shot which forced Tyler into an excellent low save.
Shortly afterwards, the keeper did well to turn a header from centre-back Dean Beckwith around a post for a corner.
In the closing stages, with Peterborough's attack still very much kept under wraps, it was still the home side that were carving out the openings.
The best of these came from substitute Luke Webb who sent a 25-yard drive flashing inches wide.