Puncheon was among the scorers against his former club, but was keen to stress the importance of the whole team's performance.
"It's always good to get one against a former club, but the most important thing was getting three points. We sort of 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 have always known as a group that we shouldn't be where we are," said Puncheon.
"There have been games that haven't gone our way and games that have slipped through our hands, but we were determined not to do that from back-to-front and in [terms of] finishing off goals and that happened. You can sit there and say it's easy, but we were on the top of our game on every yard of the pitch.
"The two midfielders covered every blade of grass on the pitch, Gaston [Ramirez] and Rickie [Lambert] both put in a lot of work as did the full-backs, centre-halves and goalkeeper. That counts, that's what it's all about and that's what we did."
The result leaves Southampton 19th in the table, but they now have a four-point gap between themselves and bottom-of-the-table QPR.