"We had time to prepare for this game and everything turned out very well, in defence and in attack. We are proud of the team. Paris played very well, but we kept their threat to a minimum," Xavi said after substitute Andreas Christensen's 77th-minute header gave Barça the victory at the Parc des Princes.
Raphinha had given the visitors the lead at half-time, only for PSG to turn the game on its head with goals by Ousmane Dembele and Vitinha in the first six minutes after the restart.
However, Raphinha volleyed in a Pedri pass to equalise before Christensen's winner.
"It is a great victory against one of the best teams in the world. It is very difficult to defend against this team because of how they press you, but we did it very well," added Xavi, whose side are unbeaten in 12 games since he announced he would depart at the season's end.
"We are only halfway there though, and it will be very difficult in Barcelona."
The Catalans are appearing in the last eight of the Champions League for the first time since 2020, when they lost 8-2 to Bayern Munich in Lisbon, and since Lionel Messi left the club.
It is their first away win in the knockout phase of the competition since 2019.
"The players believe in themselves," said Xavi as he looked ahead to next Tuesday's return at Montjuic.
"They have this opportunity, and if they play in the same way they will get chances. Nothing is done but we can be proud. This match shows that Barça are very much alive."
It was a disappointing night for PSG, with Kylian Mbappe for once failing to deliver on a big occasion.
He scored a hat-trick on the French club's last visit to Barcelona in the competition in 2021, though, and their coach Luis Enrique is optimistic that they can still progress.
"Congratulations to Barca for the victory. I think we could have got a different result but we accept the scoreline tonight and are focused on turning it around," he said after PSG suffered their first defeat since losing 2-1 away to AC Milan in the group stage in early November.
"I have no doubt that we can turn it around and that we will. That is my objective.
"We have not lost away from home in the league this season. We have six days until this game. Away goals no longer count and that helps us in this case."
He added: "We could have won this game. I am not saying the result is unfair but it came down to little details and we will work to ensure that in the return the little details go in our favour."
