The Spain international feels the former Santos man and the young defender are destined to shine this season after their performances against Celtic on Tuesday
The Brazil international and the centre-back both played an important role in a hard-fought win for Barca and Xavi feels they will prove to be key figures for the Catalans over the course of the season.
"Neymar and Bartra are showing their quality," the Spain veteran was quoted as saying on the club's official website.
"They will be important throughout the whole season and today they proved it."
A second-half header from Cesc Fabregas sealed maximum points at Parkhead after a spirited defensive showing from the Scottish champions, but Xavi believes the Blaugrana should have made the result more comfortable.
"I believe that we had a lot of possession and we dominated the match. We only scored once but we could have scored more," the midfielder added.
Barcelona sit atop of their group with six points from two games, two points clear of second-placed AC Milan.