Despite guiding Juventus to Serie A promotion after a one-year spell in the second division due to the match-fixing scandal, Deschamps handed in his resignation on Saturday.
Reports said Deschamps had a disagreement with Juventus sporting director Alessio Secco over the club's transfer policy for next season.
The 38-year-old did little to quell the rumors, hinting at an unhealthy atmosphere within the Juventus administration.
"The problem was not that I wanted to decide on everything, it was a number of different factors," he was quoted as saying by Calcio Italia magazine.
"It is true that I had difficulty this year and wanted to know how we were going to be organized next season which, I am convinced, will be very tough.
"There is a lot to be done and the fans’ expectations are high. A Coach needs to work in a relaxed atmosphere and, looking carefully at the situation, I made this decision that I consider to be in my best interests."
Former Juve coach Marcello Lippi, who has been out of work since leading Italy to the 2006 World Cup triumph, was linked with a return to the Bianconeri.
However, he denied ending his current rest period.
"Anyway my rest is not ended. I've said many times that next summer I won't coach - and the fact that Juve's bench is now free doesn't change my decision," Lippi told Gazzetta dello Sport.