After losing to West Ham and Liverpool in consecutive matches, the Saints bounced back as a first-half Jay Rodriguez strike sealed three points in south London.
Southampton dominated possession throughout and found their reward when Rodriguez got the better of Julian Speroni to slot home the only goal of the match.
Victory at Selhurst Park means Southampton have now won six games on the road - equalling the club's record in the top flight - and Pochettino believes his side were deserving of the points.
"It was a very important win," he told Sky Sports.
"I thought we played really well against West Ham and Liverpool but were not able to get anything positive out of those two games.
"It was really important to cut the run of bad results that we were in, we came to a tough stadium, played against a tough side and that adds merit to our victory."
Rodriguez's match-winner came just before half time as he got away from two defenders before taking on Palace goalkeeper Speroni in a 50-50 outside the box.
The England international came away with the ball and slid home as he sat on floor and the Saints boss applauded his attacker's work-rate.
"It showed his quality and great technique," Pochettino said.
"I'm just very happy, I'm very happy for him and very happy overall for the team.
"I think the team deserves full credit for a great victory today."
After having four players feature in England's midweek friendly against Denmark and 12 on international duty in total, Pochettino praised the concentration displayed by his side.
"I thought we were playing against a very tough team, it's very difficult to come to Crystal Palace and actually get something," he added.
"I thought the team was very well focused today and even without possession I thought it was great work from the entire team.
"We're a brave team, always looking to get on the attack, always trying to get on the counter attack and I think the team deserve great credit."