The Reds took the lead in the 67th minute when QPR defender Richard Dunne bundled the ball into his own net.
However, Vargas drew the hosts level again moments later, but the match was won in the final seconds of stoppage time when Steven Caulker scored another own goal.
Austin told BBC Sport: "We definitely deserved a point, if not three. For the first goal we witched off and for the other two they got us on the break.
"Bobby Zamora is so strong and he created a lot of chances for us. We certainly had the chances today. We know what we need to do, we need to back the manager and get a win as quickly as we can."
The result leaves QPR rooted to the foot of the Premier League table, with four points from eight games.