Rangers were moments away from sealing a hard-fought point in a madcap encounter at Loftus Road before a Steven Caulker own goal on 95 minutes undermined their efforts.
"I thought we were miles the better team. We never gave up, we kept going, I thought we were excellent," a frustrated Redknapp told reporters.
"You don't always get what you deserve, we didn't today, we deserved [something], and to get beat was an absolute injustice really."
The drama increased when Philippe Coutinho fired the Reds ahead once more in the first minute of added time, only for Vargas to head home another equaliser on 92 minutes.
Redknapp's side remain rock bottom of the Premier League table on four points following the defeat.