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."