The Spain international said Vilanova's health problems inspired the Catalans to give their all in the face of adversity.
Vilanova suffered a cancer relapse that kept him away from the Barca bench for large parts of the 2012-13 campaign, before eventually stepping down altogether at the end of the season.
"Looking back, 2013 was a very good year. We came up short in the Copa del Rey and Champions League semifinals against Real Madrid and Bayern, but it was an amazing feat to win the league the way we did, considering the circumstances surrounding Tito Vilanova’s illness," Xavi told FIFA.com. "I think that brought the squad even closer together, inspiring us to go on to win the title with a historic tally of 100 points.
"All in all, it was a great year, particularly overcoming adversity to win the league title against the backdrop of the Tito situation. That was an incredible achievement."
Vilanova was eventually replaced by Gerardo Martino at the start of the 2013-14 campaign.