The 27-year-old winger scored the only goal in a 1-0 home win against Aston Villa on Saturday, the club's third triumph in a row following successes against Chelsea and Cardiff City.
The win lifted Tony Pulis' side to 12th, seven points clear of the relegation zone, and although they have a game in hand on Fulham and Cardiff, who are both in the bottom three, Puncheon has warned against complacency.
"It's 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," said Puncheon, who joined Palace permanently in January.
"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."
Puncheon's low 76th-minute strike was his third goal in two games and his sixth in 2014, and he believes his fine form is down to confidence.
"It's just belief – you've got to believe in yourself. A few games back the manager said I had things on my mind and didn't play me, but since then I've bounced back, which has been great," he added.
"With the goal, I knew that as soon as the ball came on my side that I'd get my body in the way and look to get my shot off. That's what I've done and obviously we've scored."
Pulis lauded Puncheon earlier in the week and said he expects offers from big clubs for the player in the close-season. The player returned the praise for his manager following the victory over Villa.
"If you look at the position that we were in when he came and what he's done to this team, we all have the belief that we will stay in the Premier League now," he continued.
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