Norwich went down to 10 men after just two minutes when Martin Olsson was sent off for handling the ball on the goalline.
Tjaronn Chery failed to convert the subsequent penalty, though, sending it wide.
QPR did take the lead in the game on 21 minutes when Conor Washington found the net, and Sebastian Polter doubled the advantage six minutes later.
Steven Naismith halved the deficit for the Canaries in the 78th minute, but Rangers held on for the three points.
Former Norwich striker Roberts has taken to Twitter to give his reaction to the final result.
Don't go to games Matt but tough for him too turn this run around players need to look at themselves too https://t.co/oR2q1FGl46— Iwan Roberts (@iwanwroberts) November 19, 2016
Norwich, who were relegated from the Premier League at the end of last season, are in poor form at the moment.
Alex Neil’s side are currently sixth in the Championship table with 27 points from 17 matches.