Palace are without a win in their last three Premier League outings after a Jay Rodriguez strike sunk the Eagles in Croydon.
The hosts struggled to get a touch in the first half as Southampton dominated possession, before Rodriguez fired them into the lead, albeit in peculiar fashion.
Saints forward Rodriguez beat Palace keeper Julian Speroni in a 50-50 challenge before sliding the ball home while sat on the floor.
Defeat leaves Palace sitting precariously on the brink of the relegation zone, with just two points separating them from Cardiff in 18th and the Eagles manager understands the importance of every game in the Premier League run-in.
"Southampton have got some quality, they're a very hard-working side," Pulis told Sky Sports.
"Every game that we play at home, we have to try and get points from.
"We're disappointed to not get a point out of the game at least today, but we have to move on.
"We have got 10 cup finals now, 10 very, very tough games and they're all cup finals for us."
Rodriguez struck on the cusp of half-time as the visitors turned over a Palace set-piece to counter, with the England international skipping through two defenders before beating Speroni outside his area.
"Obviously the nature of the goals disappointed us," he said.
"It was our set piece and we've dropped it and we've failed to deal with it.
"I don't blame the defending. He's [Rodriguez] shown great commitment to challenge Speroni and to then follow it through.
"Fair play to him, you've got to give him the credit for that."
Try as they may, Palace were unable to forge a breakthrough and despite enjoying numerous set pieces as they launched a spirited second-half comeback, Pulis revealed his frustration at the lack of chances created.
"We needed a break," Pulis admitted. "We needed something to go for us but nothing did and there's a couple of things which went against us.
"The first two offsides given by the lineman, I think our player was onside.
"Little things like that, you need those breaks in these games and we didn't get them."
And keeper Speroni felt Saints had enjoyed the rub of the green, saying: "A very close match that could have gone either way. A lucky goal decided it.
"The rebound could have gone either way. He got lucky, I was unlucky and he put the ball in an empty net."