Darren Ferguson, on the other hand, endured a toothless display from his Posh side in the week he embarked on a second year of a second spell at London Road.
The result means the Tigers further consolidate their position in the play-off places, with Barmby's decision to retire from playing and concentrate on management paying immediate dividends.
Peterborough came flying out of the blocks, Emile Sinclair forcing Vito Mannone to tip the ball round the post and blasting right-footed against James Chester within minutes of kick-off.
The visitors continued to swarm the Tigers' territory, Lee Tomlin unlucky not to open the scoring with a fizzing strike from the edge of the box.
Hull enjoyed a welcome chance to regroup after witnessing Joe Newell spoon his shot over the crossbar and slowly began to get back some control.
Koren had an effort in the 15th minute, connecting sweetly with a Corry Evans cross but blasting wide of the target.
The Slovenian threatened to notch once more before his opener with a pinpoint drive from 30 yards, Gabriel Zakuani bravely stepping forward to diffuse the danger.
But the deadlock was soon broken with 27 minutes played. Aaron McLean's weighted cross was picked up in space by Koren, who took aim with a low, hard shot beyond the outstretched Joe Lewis and into the net.
And with Posh's early bluster nowhere to be seen as the interval approached, Liam Rosenior volleyed Andy Dawson's cross narrowly wide, before Lewis had his palms stung by a pacy shot from Paul McKenna.
The visitors, somewhat reinvigorated by the half-time break, began to cause problems to Barmby's charges once more.
First, Tomlin weaved his way through to summon a firm catch from goalkeeper Vito Mannone.
Next, the Hull fans gasped as George Boyd teed up a dangerous drive from 25 yards, which he managed to skew into row Z.
The Tigers, though, were content to keep their opponents at arm's length, and soon answered back as Cameron Stewart squeezed the ball through a tight gap only to whip it agonisingly over the bar.
Koren was withdrawn for Manchester United loanee Joe Dudgeon on the hour mark, the young defender almost doubling the advantage immediately as he clipped wide from six yards when perfectly placed to score.
The hosts continued to pepper Lewis' goal as the game drew to a close.
Brady and McLean produced strong saves from Lewis before Paul Taylor spurned a late chance to snatch a point in added time, Jack Hobbs on hand to confidently clear the danger.