The resounding 4-1 victory over Parma last weekend at their new stadium meant that Juventus top the table after the first round of matches on a superior goal difference.
Vidal came on to score in that match to record a goal on his competitive debut for his new club, but he is not getting carried away with success after just one match, maintaining that other clubs are also capable of challenging for the Serie A title as well.
He told Juventus' official website: "As far as the club's tradition is concerned, Juventus need to target victory, but there are many strong teams: Milan, Inter, Napoli, Lazio, Roma,
"We're preparing to face a long and hard-fought championship, but we're a team of warriors and we give everything on the pitch."
Vidal arrived from Bayer Leverkusen over the summer for €12.5million, but is not guaranteed a spot in the Juventus midfield with talents like Andrea Pirlo, Milos Krasic, Emanuele Giaccherini and Claudio Marchisio in the same side.
He commented: "At Bayer, I played a bit further forward alongside two others and with Renato in front of us, but I also feel fine playing in this position [alongside Claudio Marchisio and just behind Mirko Vucinic], because I have license to go forward,
"Competition for places? It's there, but it's not a problem. Everyone likes to be in the starting line-up, but I've only been here a short time, I'm adapting and I'm perfectly relaxed.
"When it's my turn I'll look to be ready, because when you play from the start it's important to show you deserve your place for the entire 90 minutes, not just half an hour."
Juventus will be hoping to continue their fine start to the campaign this Sunday as they travel to play Siena.