Saints' return to the top flight after a seven-year absence was hardly ideal, with just one win in 11 matches leaving them 19th.
Nigel Adkins' side shipped a league-high 29 goals in the process, but a new-found defensive resolve has resulted in a dramatic change in fortunes and they are now up to 15th in the table.
Southampton have only conceded four goals in their past six matches and collected their second clean sheet in Saturday's 1-0 win against fellow strugglers Reading.
Asked what has changed at the club, winger Puncheon said: "I think it was nerves.
"I'll be honest, as a team coming into the Premier League, I think we were a bit nervous, a bit shaky.
"We didn't find our feet or our rhythm and now we have found that and that is showing as a team.
"We haven't got a bad defence. A few of the boys playing in that back four played in the team last season and how many clean sheets were there last season? Now we are gelling and that is showing.
"It is definitely onwards and upwards now. We look forward to the Sunderland game. It is a home game so we need three points again."
Puncheon has flourished for Saints this season and scored the decisive strike on Saturday in a match in which he also saw a first-half header harshly chalked off.
"It was a deserved win," he said. "We could have won by more but we got the three points and that was the main things for us.
"I wasn't too sure at the time why my first-half goal was disallowed. The ref said there was a push but it wasn't me.
"At the end of the game everybody said it was a clear-cut goal and it should have counted.
"It was good to score, though. Me and Clyney (Nathaniel Clyne) are working up a good relationship. We're gelling, getting better and better as the games go on.
"He has picked me out really well and I have slotted it across the goalkeeper."
Puncheon's form has led to some observers touting him as a potential option for Roy Hodgson's England side.
His former boss at Barnet, Paul Fairclough, has backed him for a call-up and Saturday's performance will not have harmed his chances given England Under-21 boss Stuart Pearce was in the crowd.
"I don't worry about those sort of things. That's out of my hands," Puncheon said.
"The only thing I worry about is putting on the Southampton shirt and performing week in, week out.
"It is always nice to get mentioned but you don't let those things get in your head."
Saints now find themselves in the unusual position of having a two-week break, with their scheduled trip to Chelsea postponed due to the Blues' Club World Cup commitments.
Reading, by contrast, have to dust themselves off and go again on Tuesday at Sunderland.
Left-back Nicky Shorey is hoping for a much-improved performance from the Royals, who head to the Stadium of Light on the back of four successive defeats.
"It wasn't great," he said of Saturday's loss. "In the first half I thought we might do something but the second half all the lads can say it wasn't a good performance.
"I don't think it matters who we're playing, the performance has to be there. It hasn't been there for whatever reason.
"Some games we have been there for a while and then got slack and against Southampton I thought we were solid in the first half but well short in the second half.
"We all know we have to up our game and show a bit more on the ball because that is what this league demands.
"It is a good thing that we have a game coming quickly and hopefully we can get a result up there."