The Turkish champions will head to Turin next week carrying a three-goal cushion after a thrilling 5-2 comeback victory in the first leg on Tuesday night.
Galatasaray recovered from a difficult opening period, having gone into the break trailing 2-1, before producing a powerful second-half display that turned the tie on its head.
Goals from Noa Lang and Davinson Sanchez inside the opening 15 minutes of the second half handed Galatasaray a 3-2 lead by the hour mark, shifting momentum firmly in their favour before they added further goals to establish a healthy advantage.
Juventus, however, had earlier shown their threat with a swift response of their own. After conceding the opener to Gabriel Sara, the Italian giants struck back emphatically through a Teun Koopmeiners brace during a dominant 17-minute spell in the first half, briefly seizing control of the contest.
Speaking ahead of the return leg, Osimhen - who registered two assists in the first leg - stressed that the scoreline does not fully reflect the challenge that awaits his side in Turin.
"I mean, we all know why I took the ball. 3-2 is not enough against this kind of team," Osimhen said, as quoted by Forza Cimbom via Pan Africa Football.
"This is Juventus, one of the best teams in the world. Italian teams are always capable of surprises and they have the quality."
The Nigeria international explained that his insistence on pushing for more goals was driven by the need to weaken Juventus psychologically before the second leg.
"To make them weaker, you have to score more goals," he added.
"There is still another game to play in Turin, and for me it was important to push my teammates and make sure we kept scoring."
While Osimhen described the performance as one of Galatasaray's best in the competition, he insists focus must remain sharp.
"We deserved the win, but Juventus are a great side. We still have to show up in Turin," the striker concluded.
The return leg will be played on Wednesday, with Galatasaray aiming to seal progression to the next round.
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