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Memphis Depay scored the all-important away goal for Lyon from the spot after a controversial penalty was awarded in the 12th minute.
Despite Cristiano Ronaldo's best efforts to get Juve back into the match - converting a own spot kick just before half-time and scoring a long-range stunner in the second stanza - Sarri's side couldn't get another goal to ensure qualification and a quarter-final against Man City.
Even though his team achieved Juve's worst finish in the competition since 2015-16, Sarri was happy with the efforts by his players.
"I thought we put in a great performance this evening," Sarri said to Sky."The team has revitalised itself over the last few days, and if they weren’t devastated in their confidence by the elimination, I’d be very satisfied with their performance.
"If I take away the huge disappointment at the elimination, then I am very happy with the team this evening, as they showed character and gave their all. If we hadn’t been eliminated, I’d return home happy tonight."
Bosnian midfielder Miralem Pjanic, who played his last game for the club before joining Barcelona for next season,hinted that he was unhappy with a lack of playing time under Sarri and revealed the Italian's management of the side has been much better to the period when he was coaching at Napoli.
“The last few months haven’t gone the way we wanted to, for reasons I still haven’t been able to understand. I wanted to play more, that’s for sure,” he told Sky Sport.
“Considering the way the coach played at Napoli, where everyone was involved and fully committed to that project. We played a different type of football, I am not the only one to say that, it’s obvious. It takes time to develop that.
“Winning is not simple. We made it look simple in recent years, but it’s becoming a fight with many other teams. This club must continue to do extraordinary things, and much more in Europe.