The 27-year-old scored the only goal of the game against Aston Villa on Saturday afternoon to secure a 1-0 victory for Palace, which moved them 13 points clear of the bottom three.
Despite this, Puncheon is quoted by the Belfast Telegraph as saying: "We're not safe until it's mathematically impossible to go down.
"We've just got to keep going until we reach that point. We don't get carried away. Those games are gone. We've got to go to Everton and then West Ham after that, so we've got two tough away games in the next week.
"It was a great win, just like the two we had before, but we've got to forget about that now and look forward to Everton on Wednesday."
Puncheon has made 31 appearances for the Eagles this season, scoring six times in the process.