The Saints are playing in the Premier League for the first time since 2005 and a 1-1 draw at Sunderland on Sunday all but secured top-flight survival.
Only a mathematical miracle next weekend will see the South Coast club drop four places and end the final day in the bottom three.
It represents a fine achievement for a team that was playing League One football just two years ago and lost their first four league games of this campaign.
Former Plymouth and MK Dons star Puncheon, who scored in Sunday's clash at the Stadium of Light, believes they deserve their Premier League status for the way they have improved as the season has progressed.
"It's a massive feeling knowing that it's more or less there," he told the Daily Echo. "For the season we've had and the way we've gone about it it's even better, because we deserve it, as a group of players and as a football club.
"It was a tough start for us [this season]. We've learnt our lessons and we've grown as a football team and a football club, and that's shown.
"That's why this was important for us to obviously get the points on the board."