The Bianconeri’s poor defeat leaves them third in Group H with one win from four games, sitting five points behind Paris Saint-Germain and Benfica in the top-two spots in the group.
Juve are also under-performing domestically, fresh from a 2-0 loss to AC Milan which has them eighth in Serie A with 13 points from nine games.
“Massimiliano Allegri is our head coach and he will stay,” Juventus president Andrea Agnelli told Sky Sport.
“I feel ashamed and angry so in this kind of situation you cant blame one single person, its the whole group.”
Allegri, who guided Juve to a fourth-place finish last term after replacing Andrea Pirlo, vowed to stay with the club.
“The president is right to say that we should be ashamed,” Allegri said.
“This has been one of the worst days of recent times, and staying together will do us well to work, rest and reflect.
“I’ve never thought about resigning, because the more difficult the challenge becomes, the better the feeling to overcome it. This thought must enter everyone’s heads so that we respond with courage, desire and passion.”
On the loss, Allegri added: “All we can do is keep quiet right now. Our performance was not up to par, especially from a character point of view.”