Puncheon, who spent the first half of the 2011-12 season on loan with Rangers, scored his side's second in a vital 3-1 victory over the Barclays Premier League's bottom team.
"It's always good to get one against a former club, but the most important thing was getting three points," the wide-man told Saints Player
after the game.
"That's what we did, so it was good. We got on the front foot and did what we've been doing in recent weeks.
"I thought we were solid, and that showed in the first half – and the second half. We were on the top of our game in every yard of the pitch."
Rickie Lambert had put Saints in front before Puncheon doubled the visitors' lead before the half-time interval.
Junior Hoilett looked to have set up a nervy second period when he halved the deficit three minutes after the break, but Nigel Adkins' men quickly resumed their dominance.
Their eventual 3-1 win – topped off by Anton Ferdinand's late own-goal – moves them to within a point of safety and leaves their hosts four points adrift at the foot of the table.
And Puncheon said after the game that he and his teammates were determined to show their league position was a false one after a number of narrow defeats earlier in the season.
"As a group we've always known that we shouldn't be where we are," he insisted.
"There are games that haven't gone our way and games that have slipped through our hands, but today we were determined not to do that from back-to-front and in [terms of] finishing off goals, and that happened.
"It's a good feeling, and it'll be a good feeling tonight and tomorrow until we come back into training next week."