The former Stoke boss – who was announced as Ian Holloway's successor last weekend – saw his men fall to their 10th Premier League loss of the campaign after a first-half goal from Gary Hooper.
The striker netted his second league goal for the hosts in the 30th minute, after some impressive build-up play from Wes Hoolahan.
Pulis will take some positives from the defeat, however, after a battling display - and he will have an almost immediate chance to seek a response when Palace host West Ham on Tuesday.
The 55-year-old opted to make just two changes from the side that he had watched beat Hull City 1-0 last Saturday, with Yannick Bolasie's suspension seeing Jason Puncheon called in, while Cameron Jerome replaced Dwight Gayle.
Injury concerns played into Norwich boss Chris Hughton's selections, with three changes from their 2-1 loss to Newcastle United including a return for Sebastien Bassong, who made his first appearance since November 2.
The 27-year-old almost marked his comeback with a goal within the first minute, but headed wide.
Seven minutes later, the hosts looked to have taken the advantage when Leroy Fer jumped higher than the Palace defence to head at goal, only to see his effort bounce down off the crossbar and onto the line, with goalline technology showing that it had not crossed.
Hughton's men continued to apply the pressure, however, and they were eventually rewarded in the 30th minute when Hooper fired into an empty net after getting on the end of a fine pass from Hoolahan.
Palace responded and Barry Bannan was denied an equaliser by first the crossbar and then Martin Olsson in the 32nd minute as the visitors entered the break behind.
Pulis' words at half-time clearly had an effect, as his side quickly upped the pressure at the start of the second half, although they struggled to carve out clear-cut chances.
Hoolahan squandered the best chance of the early part of the second period at the other end, as his weak shot was easily saved.
The hosts were almost made to rue that missed opportunity just a few minutes later, when Bannan's cross skidded across the face of goal before Bassong just managed to wrap his foot around the ball to send it over the crossbar.
Palace had another chance to grab an equaliser in the 82nd minute, but substitute Jimmy Kebe – who had come on just six minutes earlier – saw his strike graze the outside of the post.
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