Back-to-back wins over Chelsea and Cardiff City have lifted the Eagles up to 14th in the Premier League table, seven points clear of the relegation zone with a game in hand over two of the bottom three.
Pulis believes that the fans have played a major role in the team's recent upturn in form, but warned that they are not safe from relegation yet and talked up the importance of their match against Aston Villa next weekend.
"Right from the terraces the crowd have picked it up and they've been wonderful, especially the home games which we need to win and we need to pick points up," Pulis is quoted as saying by PA.
"The players have responded to it and it is almost like we have started a little fire and it has just got bigger and bigger. But as I've said, I am very, very conscious that we haven't got to that stage yet where we can say we've stayed up. We still have a lot of work to do.
"We've got six games to go to get the points that we need. We are still not safe, we still need points, so next Saturday's game against Aston Villa is a massive game for us."
Palace have never managed to stay in the Premier League for two consecutive seasons.