Lemina netted in the seventh minute with a diving header after Victor Osimhen headed a corner back across the goal.
The midfielder later expressed gratitude to teammates and fans after earning the Player of the Match award.
Lemina said the team fought hard for victory, similar to their earlier meeting during the league phase.
The result mirrored the sides’ previous encounter in September, when Galatasaray also won 1–0 through an Osimhen penalty.
Liverpool manager Arne Slot described the outcome as disappointing after taking charge of the club for the 100th time.
He said Liverpool created several chances and could have scored more despite the defeat.
Both teams had goals ruled out late in the match following decisions by match officials.
Osimhen thought he had doubled Galatasaray’s lead just after the hour mark.
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However, the goal was disallowed after Baris Alper Yilmaz was judged offside in the build-up.
Liverpool also had the ball in the net in the 70th minute following a goalmouth scramble.
The effort was cancelled after a VAR review showed the ball had struck Ibrahima Konate’s hand before entering the goal.
Liverpool started brightly and created several early chances before Galatasaray gained control after scoring.
Goalkeeper Giorgi Mamardashvili produced several important saves to keep Liverpool in the contest.
Galatasaray goalkeeper Ugurcan Cakir also denied Hugo Ekitike with a fine save in the closing stages.
Liverpool captain Virgil van Dijk admitted his side created chances but failed to convert them.
He, however, remained optimistic about Liverpool’s chances in the return leg next Wednesday.
Van Dijk said playing the second leg at Anfield would provide an advantage for Liverpool.
Galatasaray reached the last 16 after defeating Juventus FC 7–5 on aggregate in the playoffs.
Liverpool qualified directly for the knockout stage after finishing third in the league phase.
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