The experienced midfielder says his team is comfortable with its lead over Real Madrid and hailed Neymar's goal as crucial to the eventual outcome
Neymar and Alexis Sanchez scored the goals for the hosts, before a last-gasp consolation by Jese Rodriguez wrapped up the result.
And although Xavi is happy with the result and his side's Liga standing, he called for an improvement in order to remain at the pinnacle in Spain.
"We were the better side and for that reason we are quite happy, but we have to improve a lot of things," the 33-year-old told reporters.
"This can be done through playing, and now we are six points ahead of Real Madrid we can be quite relaxed about it.
"Real Madrid is a side with excellent players. But we were in charge, and Neymar's goal gave us a lot of confidence. In a Clasico, going into the lead is 70 percent of the battle."
The veteran midfielder also commented on complaints by Madrid players, who claimed a challenge by Javier Mascherano towards Cristiano Ronaldo should have been a penalty kick.
"You can say that it was either a legal charge or an illegal one. The referee did not blow for it and so it was all the better for us," he added.
Barcelona is on the top of La Liga, with Atletico Madrid trailing by a point thanks to its 5-0 trashing of Betis on Sunday.