Spanish champions Atleti fell to a 3-2 defeat at the Karaiskakis Stadium in Tuesday's Group A opener despite controlling large parts of the game.
Atleti, who were beaten finalists by rivals Real Madrid last season, never really recovered from going two goals after 31 minutes, Arthur Masuaku's driven effort and a composed finish from on-loan Barcelona midfielder Ibrahim Afellay doing the damage.
Mario Mandzukic's header reduced the deficit before the break, but Kostas Mitroglou re-established the two-goal cushion in the second half - and that proved enough despite substitute Antoine Griezmann's late consolation.
Midfielder Koke has pinpointed Italian champions Juve, who were 2-0 victors over Malmo in their first match, as Atleti's biggest threat in the group and urged the team to bounce back strongly when the Turin side visit the Vicente Calderon on October 1.
"We knew that this was a difficult group, and the fans here really get on top of you," he told reporters.
"We have to keep on working hard and think about our next game, at home to Juventus, who are our biggest rivals in the group."
Reflecting on the Olympiacos match, Koke felt that Atleti made too many errors throughout.
"I think we made some errors," he added. "They were very focused and capitalised on our mistakes.
"We knew that they were going to put us under a lot of pressure with their fans behind them; they scored very early on and it's always difficult when you go 2-0 down."
