The Spanish side enjoyed 89% of possession at Parkhead but were ultimately undone by the Scottish underdogs.
"I think we deserved the victory," Vilanova told reporters. "We tried everything until the end. We have only conceded two corners, and they scored from one of them.
"We must also congratulate Celtic for their good game, for winning and for their spectacular supporters."
Despite Wednesday's defeat in Scotland, Barca still top Group G by two points.