Despite almost constant pressure Rovers failed to open the scoring until the 64th minute when Matt Jansen fired home at the second attempt from close range.
Game on as they all only needed to find another goal and they would be through.
Unfortunately for Graeme Souness' side less than 60 seconds later the Turks capitalised on some casual play by stand-in Blackburn right-back Steven Reid and handed Mustafa Ozkan a leveller.
Rovers hit the woodwork three times; Jansen after nine minutes when he swivelled and shot from close range; a wonderful crashing shot from David Thompson that rattled back off the underside of the bar and finally a Tugay drive in the dying seconds that deflected off an opponent but still failed to find the net.
Indeed, if Italian misfit Corrado Grabbi had taken any of the numerous chances that fell his way throughout the game, Blackburn would be sitting pretty in the draw for the second round on Friday.
As it is, it will be Genclerbirligi who will take that place as some desperate defending and quite extraordinary goalkeeping by Damir Botonijc prevented Rovers from getting the goals their overall play and possession merited.