Gary Hooper's goal on 30 minutes proved enough to give the Canaries a much-needed victory, which handed under-pressure Chris Hughton some breathing space following seven Barclays Premier League defeats before Saturday afternoon.
However, the Eagles - boosted by last weekend's away win at Hull - were probably worth a point, particularly for their second-half efforts, and had seen a shot from Barry Bannan headed onto the crossbar by Norwich defender Martin Olsson while, with just a couple of minutes left, Cameron Jerome missed his kick when in front of goal.
"You have to take your chances. We did not have the breaks today," said Pulis, whose appointment was confirmed just ahead of the Hull game.
"How the hell (Norwich defender Sebastien) Bassong gets that (clearance) over the crossbar from there, it was unbelievable, and then the kid who stops Barry's shot from going in with his header, Cameron had a really good chance, so we have had the opportunities.
"But I can't fault their work-rate, they gave it everything, but you need a break and we did not get that."
Sunderland's goalless draw at Aston Villa pushed Palace back to the bottom of the table, but they are not yet cast adrift ahead as the south London outfit prepare for key home games against West Ham and then Cardiff.
"There are certain clubs we cannot compete with, and there are others we have to compete with so against those you have to give a performance," added Pulis, who left Stoke at the end of last season.
"We have come away from home and done that because we dictated the game for long periods.
"The quality at times, I was very pleased with.
"But it is going to be tough. We have a mountain to climb in a lot of respects, but it is not the first time I have been in this position."
- Sports & Recreation
- Barclays Premier League
- Barry Bannan
- Cameron Jerome
- Chris Hughton
- Gary Hooper