Juve began the 2015-16 campaign with one win in their opening six matches, but since late October they have turned their domestic form around - winning seven in succession.
That form has seen them surge up the table to within three points of leaders Inter, and Evra claims the run of results has forged a renewed faith in the ability of the squad.
"Psychologically there was something wrong," he told Sky Sport Italia. "[But] now we're going in the direction we wanted at the start of the season.
"I've always believed that when you play for Juve, the goal at the start of the year is to win the title and a lot of trophies.
"I believe in my team-mates, I believe in this club and I think we can do something great.
"I've always compared us to all the other teams, and the other teams can win the title, but of the teams I've played against I'd say the most dangerous is Juventus.
"I don't think that's arrogance, because I totally trust my team-mates, and if we give our all we'll reach our objectives."
Juventus are at home to struggling Hellas Verona when Serie A resumes on January 6 and will be aiming to close the gap at the top of the table.