A much-improved showing versus the Swans looked to have Adkins' men on their way to a second win of the Barclays Premier League season.
However, a late defensive lapse – coupled with some dubious refereeing decisions – allowed the visitors to take a point from their visit to St Mary's.
But, looking ahead to Saturday's visit to the league's last-placed side, the gaffer insisted his players have taken self-belief and confidence from their previous fixture.
"We've looked at our last performance and it was a good one," Adkins told Saints Player
"I believe we're improving all the time and we do look like a team. I thought we had a good shape about ourselves last week.
"There's a positivity, a focus and a confidence about the players so we'll move forward to the next game.
"We're taking a full allocation so there's [also] a confidence about the supporters that we're going to give it a right good go."
On the subject of the perceived refereeing injustices that denied Saints skipper Adam Lallana one – if not two – penalties last weekend, Adkins admitted he hoped there would be a touch of luck coming his side's way in the near future.
"I do believe that we'll get our fair share of decisions – they say they even themselves out over the course of a season," he said.Referee Andre Marriner says no to Adam's penalty appeal
"Sometimes you need a little bit of fortune to go your way with a decision.
"We are respectful of referees – I think that's important – but, likewise, you want a decision to go your way. I'm sure that eventually one will."
With Saints and QPR currently occupying the Premier League's bottom-two places, many have already been quick to point of the magnitude of Saturday's fixture.
However, Nigel insisted his side would approach their trip to Loftus Road in the same way they would any other game at this level.
"Every game in the Barclays Premier League is a big game," he stated.
"We've seen that already, and we'll see exactly the same for the rest of the season. They all have the same significance and importance.
"We could be in the bottom two, top two or the middle – we need to go and get three points. We're going to go away from home and strive to get our first away victory of the season."
Saints trained with reduced numbers in the early part of the week, with some of the players away on international duty.
James Ward-Prowse and Nathaniel Clyne have returned from playing for England's Under-19s and Under-21s respectively, with the likes of Steven Davis, Maya Yoshida, Gastón Ramírez and Emmanuel Mayuka now also on their way back to Southampton.
"We've been in contact with everybody and we expect them all to be fit," said the gaffer. "Some of them don't arrive back until Friday, but we've had an excellent week's training.
"There's been a good focus about the players – there's a confidence and a determination although we've had a couple of players away.
"The lads who've been with England have returned early, and the lads who've been at the training ground have trained with the right intensity and focus.
"Spirit is high, confidence is high and focus is bang-on."
Rangers have yet to win a league match this season, with their home form the worst in the division.
However, Adkins is expecting a fierce atmosphere on Saturday: "It's a great place to go to because the crowd is right on top of you and the pitch is very enclosed," he said.
"You need cool heads, but you've got to have a passion about you as well so we'll certainly endeavour to do that at the weekend.
"I've enjoyed going there previously, and I'm sure the players will do. It's going to be a good game.
"We'll want to play football, they'll want to play football and we've both got talented players. We're going to go there and strive to get three points."