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.
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.
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.
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.
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.
