It appeared as if QPR, despite being second best for much of the game, had salvaged a point when Charlie Austin equalised with a brilliant volley after Ryan Bertrand had put the hosts ahead at St Mary's Stadium.
Yet a wonderful overhead kick from Southampton striker Graziano Pelle sent the visitors home empty-handed, although QPR were unfortunate not to level as Niko Kranjcar hit the bar with a free-kick five minutes from time.
The result keeps the London club on just four points from their first six games, but Redknapp was pleased with the effort of his players against his former club.
"It [Pelle's goal] was a fantastic finish wasn't it?" Redknapp said. "There wasn't an awful lot we could do about that to be fair. It was a great technique and a great finish.
"We kept going, I thought we come back strong, never gave up. We felt we had some opportunities, [we] just needed a little bit of luck.
"There is still lots to work to be done with the team, we can only get better."
One of the bright spots for QPR was the showing of striker Austin, who Redknapp feels can be a prolific goalscorer in the Premier League after spending his entire career in the lower tiers.
Redknapp added: "It was a great finish, he's proven that he can score at this level, that was encouraging."
