Hodgson was chosen as the man to replace Frank de Boer on Tuesday evening after the Dutchman was sacked after just four games in charge. De Boer oversaw four losses in his short spell as manager, the latest away to Burnley last weekend which left Palace bottom of the table.
The 70-year-old boss has been out of a job since stepping down as England manager after a disappointing Euro 2016 where England were eliminated by Iceland in the Round of 16 stage.
But Puncheon is convinced the former England manager, who has also had spells at Premier League club Liverpool, West Brom and Fulham, has the quality and managerial experience to lift the Eagles.
"He comes with a wealth of experience," Puncheon told 'Sky Sports News'.
"He's managed some big, big players and he's managed in a wide range of leagues. He was the national manager for our country and that speaks volumes for itself.
"Structure is [going to be] important to help us push forward. We've got good players and we've got a good structure that has helped players grow and improve in the past."
Palace have not yet managed to score a goal this season and have conceded seven goals in their opening four games.
The Eagles host one of Puncheon's former clubs in Southampton on Saturday and the Palace captain is targeting a win and a clean sheet to get the Hodgson era off to the perfect start.
"Ultimately we need to win the game," he said. "We need three points he knows that and as a group of players we know that.
"As long as we leave that game with a clean sheet we've got a point."