Julian Draxler and Moise Kean scored either side of Rony Lopes' fine strike at the Parc des Princes as PSG – who were without the injured Neymar – claimed an eighth win in their last nine games across all competitions.
The result lifted the defending champions to the summit of Ligue 1, although Lyon and Lille could move back above them if they overcome Montpellier and Brest respectively.
PSG did not have it all their own way against Nice, who had 13 shots on goal, but Pochettino was pleased with his side's ability to carve out maximum points.
"It was a professional display; solid but not brilliant perhaps," he told a media conference.
"But given the circumstances, it's a decent match. It is not always easy to find the expected combinations.
"We must be ready for the competition because it is not waiting for us and we must win all the matches that come up."
Kean followed up his winner in the midweek Coupe de France victory over Caen with another decisive goal – his 10th in Ligue 1 this season – and Pochettino was impressed with the youngster's contribution.
"I think he had a good game and he scored," the former Tottenham boss said. "I'm happy with his performance; he can play anywhere in the attacking frontline. We are satisfied with everything he does."
PSG switched to a 4-3-3 formation in the closing stages and Pochettino said tactical flexibility is something he wants to instill in his players.
However, he acknowledged there will be little time for that during the quick turnaround ahead of Tuesday's Champions League last-16 first leg against Barcelona.
"We want the team to be able to communicate, to be confident in different patterns, to find new offensive animations," he added.
"After that, it's not always easy to work a lot in just 40 days [since he was appointed]. By Tuesday, there will not be much time to work tactically; we will instead focus on physical and mental recovery.
"We have to play in different animations, with different options. It was one of my goals in Southampton and Tottenham and that's also what we are trying to do in Paris: make players feel confident in different systems with offensive and defensive animations."