Allegri expects Juve to progress
The Serie A champions suffered a second successive 1-0 loss in Europe's premier club competition courtesy of Pajtim Kasami's first-half strike at the Karaiskakis Stadium on Wednesday.
Olympiacos were indebted to goalkeeper Roberto, who produced an outstanding second-half display to thwart the Turin giants.
Juve are now third in Group A behind Atletico Madrid and Olympiacos, but coach Allegri expects his side to progress.
"I'm full of optimism and I'm convinced we'll manage to go through." he said.
The former Milan coach, however, knows Juve must raise their game in order to turn around their fortunes in Europe.
"We didn't play well in the opening period. We were stretched and unable to get at them high up the pitch. Technically we were poor." said Allegri.
"We fell behind but then after the break we pushed up more. We need to improve in certain areas, against teams like this who chase and harry a lot. Even if you're not on your game, you can't let them have three or four breaks like we did.
"They pressed us a lot and the whole team generally found it hard. We needed to show more movement when we were in possession but we didn't do that."
Andrea Pirlo was substituted early in the second half, but Allegri backed the playmaker to come good.
Allegri said: "Unlike some other players, I think Andrea needs to be playing to find his best form. I thought he would be key to slowing down the tempo of our opponents.
"In any case he'll soon be bang on form again. He has a starring role to play for us in Serie A and our Champions League campaign."