The home side fell behind inside eight minutes when Brett Holman finished from close range to give Paul Lambert’s side the lead.
QPR were by far the more dangerous in the second half. Clint Hill struck the post, while Samba Diakite and Ryan Nelsen both spurned chances to give the west London outfit their first Premier League win of the season.
“We played well, and after a difficult start we came back and dominated the game, we had all the chances and deserved to win the game,” Redknapp told BBC Sport.
“We just couldn’t get the second goal. We are in a difficult position but you’ve got to keep believing, working hard, we need that first win to get us going.”
QPR are still to secure a victory this season after 15 Premier League games, matching Swindon’s winless record in 1993 and leaving the Hoops seven points behind 17th-placed Sunderland.
However, despite the setback, Redknapp refused to be downbeat and the former Spurs manager is targeting their first victory at Wigan Athletic next Saturday.
“We needed it today but it didn’t come and we need to try hard to get it next week against Wigan,” added Redknapp.
MORE: The latest football news