Mark Hughes' side had already beaten Wisla Krakow and FC Basel in Group E, meaning a point from their trip to Rotterdam was enough to progress.
The visitors created the first openings of the game, with the out-of-form Shabani Nonda twice failing to capitalise on good work from strike partner Benni McCarthy, who troubled the home defence throughout.
However, just before the half-hour mark Feyenoord threatened as Greece's Euro 2004 hero Angelos Charisteas forced a fine block from Rovers keeper Brad Friedel.
Five minutes before the break Andre Ooijer denied his compatriots, as he cleared a Nicky Hofs effort away from the danger area to keep Rovers on level terms.
Straight after the restart Feyenoord were handed a chance to break the deadlock, as Zurab Khizanishvili's slip allowed Charisteas through on goal, but again Friedel was equal to the task.
Brett Emerton went close for Rovers against his former employers and midway through the second period, Feyenoord thought they should have been awarded a penalty when Ooijer appeared to handle in the area.
However, from that point on Rovers denied the hosts of any clear sights of goal and Robbie Savage almost struck the winner eight minutes from time, only to shoot wide from McCarthy's pass.