The result lifted Palace up to 14th, seven points clear of the Premier League relegation zone, and Pulis was delighted his side did not let their surprise 1-0 win over Chelsea last weekend go to their heads.
"You get a great result against Chelsea and it's a little like after the Lord Mayor's show," he told reporters.
"We've been banging on about that all week – not taking our foot off the pedal. We've gone out there and we haven't let that happen."
Victory over Cardiff was aided by Palace's third clean sheet in four games, and Pulis explained tightening up the defence had been a priority when he replaced Ian Holloway as manager in November.
"When I took over we were conceding a lot of goals," he added.
"We were conceding a lot in the early stages of games. To stay in games you have to keep it tight. Clean sheets for us are very important.
"We defended fantastically. They sent a lot of balls into the box, but we dealt with everything. The two central midfielders were fantastic too, and we looked good on the break."
Palace's biggest threat on the counter-attack at the Cardiff City Stadium was Puncheon, who opened the scoring with a firm low drive before sealing the win with a brilliant 20-yard strike after Joe Ledley had made it 2-0.
"In the first 10 minutes, 15 minutes, [Puncheon] was so sloppy," said Pulis. "But he's a wonderful player, he's got great ability. I was very happy with the two goals.
"But we've got a lot of work to do [to stay up]. Some results today have brought the pack together."