Juve were hammered 4-0 in their latest preseason friendly.
Danilo said: "Surely there is the tiredness we have on the tour in America, with nine hours of time zone I had difficulty sleeping together with other teammates. We are working a lot in recent weeks with even double training sessions.
"We have to learn from these teams: Barca, Real and Atletico have the history of competitiveness. It is a result of the pre-season, but we must work to improve.
"Certainly we must not underestimate this. We must be careful. In football it is not enough to play well and have clear ideas. We must be more nasty and fight for every ball. We are Juve and we wear a heavy shirt in world football.
"We must take the right responsibilities: the fans who support us expect a better season than last year."