Vilanova takes charge of the favourites for the first time in the tournament having stepped up from assistant manager to succeed Pep Guardiola at the end of last season.
"In the Champions League you have to be on your guard from the start. We know this from experience because we have suffered in the past during the group stage," he told a news conference on Tuesday.
"The first match at home is very important so you don't start on the back foot. Barça have felt very comfortable in the Champions League in recent years but we know it's tough. The key thing is to take each game at a time."
Barça won the first and last of their four continental crowns at Wembley Stadium in London, at the old arena in 1992 and at the remodelled version in 2011, with triumphs in Paris in 2006 and Rome in 2009 in between.
Vilanova said it was too early to start thinking about winning a fifth at Wembley in May, when the stadium hosts its seventh European Cup final.
"If we have the good fortune to get to this stadium that holds such good memories for us then we talk about it," he said. "Right now it's too soon."
Barca are the only team in Spain to have won all four of their domestic league matches while Real Madrid have won one, drawn one and lost two, already putting them eight points behind their arch rivals.
However, Vilanova said a good start in La Liga had no bearing on the Champions League.
"There is no point in looking backwards, either when you are winning or when you are losing," Vilanova said.
"It's a different competition, I'll talk about La Liga again on Friday."
Group G is completed by Benfica and Celtic, who meet in Glasgow on Wednesday.
