Can claims that conflicts with what he was promised just days ago and insisted he "must and will" play in the competition, an indication he could push for a move in January.
The selection setback comes after former Liverpool player Can held talks with Paris Saint-Germain, only to decide to remain with the Italian champions.
"I had a talk with the club [PSG]. In the end I decided with the club [Juventus] that I would stay. And as you can see, I'm not in the squad for the Champions League," Can said, before training with Germany on Wednesday.
"I was extremely shocked yesterday because I was promised something else last week. They told me something else.
"If I had drawn my own conclusions, I honestly wouldn't have stayed. Because for me it was a condition to play in the Champions League.
"The shock is extremely deep in me. I can't explain it to myself. I have no idea why, because last year I played very well, especially in the Champions League. There has also been no justification until now."
Head coach Maurizio Sarri picked close-season signings Adrien Rabiot and Aaron Ramsey ahead of Can in his midfield ranks for the European games, with Juventus due to play Atletico Madrid, Bayer Leverkusen and Lokomotiv Moscow.
"I got a call yesterday. The phone call was not even one minute long," said 25-year-old Can. "And I was simply told that I was not there. Although they told me last week that I will play 100 per cent in the Champions League.
"I must and will play in the Champions League. I will talk to the club when I come back. And I will see what happens."