Juventus won 2-1 on Friday, but it was the French club that went to the quarter-finals.
Andrea Pirlo became Juventus' new manager hours after the club announced that Maurizio Sarri was fired.
Pirlo, a former World Cup winner, was the club's under 23 coach and has signed a two-year contract, Juventus announced.
Sarri's sacking came less than 24 hours after Juventus was surprisingly eliminated from Champions League by Olympique Lyonnais, which had finished only seventh in France's Ligue 1 this year.
Juventus won 2-1 on Friday, but it was the French club that went to the quarter-finals - thanks to the away goal scored in Turin - after beating the Italian club 1-0 in the first leg.
Sarri's spell at Juventus lasted only a year, a change from his predecessors Massimiliano Allegri and Antonio Conte - who sat respectively on Juve's bench for five and three seasons.
Sarri led the club to its ninth national title in a row - an all-time record for Italy's Serie A.
But he failed to achieve Juventus' main goal: the Champions League, a title missing in Turin since 1996, despite Juventus playing five other finals in 1997, 1998, 2003, 2015 and 2017.
Sarri also lost the Italian Super Cup to Lazio as well as Italy's cup final to his former club Napoli.
Many Juventus fans on social media appeared to welcome the club's decision.
Some of the names circulating in the Italian media before Pirlo was named included former Tottenham manager Mauricio Pochettino, Juventus legend and even current Inter boss, Antonio Conte, amid a rumoured spat with the management of the Milanese club.