Pulis calls for ruthlessness
Jay Rodriguez scored the only goal of the game when a poor header by former Southampton midfielder Jason Puncheon led to the England striker getting the better of goalkeeper Julian Speroni in a 50-50 challenge and rolling the ball into an empty net.
Pulis was content with Palace's overall performance, but feels his players need to offer more of a threat in front of goal.
"I thought we did alright," Pulis said after the game. "We competed very well, but the disappointing thing was that we never created more opportunities.
"But they (Southampton) are a good side; they've got some good players. We've watched them the last three games they've played. They played at West Ham and played exceptionally well but got beat 3-1.
"They've got some real quality and it was always going to be a tough game. In tough games, you need a break and we didn't get a break today.
"If we would have got that, I think we would have relaxed a bit more and we might have created more opportunities."
Pulis dismissed claims that Southampton's goal was "comical" on the part of Palace, instead choosing to praise Rodriguez.
"I think you've got to give Rodriguez a lot of credit," continued Pulis. "The kid showed a great appetite to get there initially ... and he's had the tenacity and energy to get after it and win a challenge with Speroni.
"That was the difference in the game."
Palace visit fellow strugglers Sunderland next weekend, and Pulis knows his players cannot afford to take their eye off the ball in the fight for survival.
"The most important thing is that you stay really focused," he added. "The lads are very, very disappointed because they've worked very hard today and got nothing out of it, but that's the Premier League for you.
"They've got to understand there is quality in every team you play and you have to really be on your mettle – you've got to concentrate for 90 minutes to get those results."