The Moroccan's spot-kick was saved by Mark Bunn after the goalkeeper had tripped Jamie Mackie in the area during the second half.
Despite good efforts from both teams, heroics from the keepers kept the scores level and Harry Redknapp's side bottom of the table.
Redknapp named two deadline-day signings in the starting line-up, with Christopher Samba coming straight into the center of defense, while Andros Townsend was thrown in at the deep end on the wing.
Norwich's own deadline day recruit Luciano Becchio started his Canaries career on the bench, with Hughton opting for an unchanged lineup to the side that drew against Tottenham at Carrow Road on Wednesday.
Both sides had early chances, with Taarabt screwing a shot wide after some good footwork, while Wes Hoolahan blazed over from right in front of goal, though he was flagged for offside.
Taarabt came close after 10 minutes following more typically sublime footwork, but dragged his shot just wide of Bunn's right-hand post, before playing in Mackie for a shot across the face of goal after 15 minutes.
The rest of the first half was fairly low on quality in the final third, with a succession of moves failing for both sides and neither goalkeeper tested beyond simple catches and claims.
The hosts had a few free kicks from distance that were whipped in by Taarabt, but they were well dealt with by the Norwich back-line before referee Jonathan Moss blew for half-time.
The second half burst into life after good work from the away side, with Snodgrass' cross flicked on towards goal by Hoolahan, only for Julio Cesar to spring to his right to stop it.
Then QPR and Taarabt wasted their best chance of the match. Mackie was sent through, and as he got to the ball was tripped in the area by Bunn. Moss pointed to the spot, awarding a booking to the goalkeeper in the process.
Taarabt looked calm, stepped up and hit a decent effort away to Bunn's left, but the keeper got down well to make a great stop.
Despite late pressure from both teams, including another couple of fine stops from Cesar, firstly from Howson and then from Snodgrass, neither team was able to break the deadlock.