Redknapp told reporters: "We came back strongly after their goal and I felt we had every opportunity at that stage of the game but their centre-forward produced a world-class goal. Niko Kranjcar hit a fantastic free kick but it hit the woodwork and we couldn't get the break.
"We didn't give up today and it was a much better performance. Charlie [Austin] took his goal well today and that's encouraging. He's proven that he can score goals in the Premier League.
"Southampton are a good side but I felt we stuck at it and we got a bit more belief in ourselves today and we've got to continue to believe."
Next up for QPR is a trip to West Ham United on Sunday.