An entertaining 1-0 first-leg win in Istanbul on Tuesday night, in Arne Slot's 100th match as Reds boss, has given the Turkish champions the advantage in this round-of-16 tie.
"What I do know is now it's halftime," the Liverpool coach said.
"We've lost here twice with 1-0 and the good thing is the next game is not played here. It is played at Anfield and our fans can create a similar atmosphere."
Elsewhere, German giants and runaway Bundesliga leaders Bayern Munich stormed to a 6-1 win against Atalanta in Italy.
Plenty of goals too in Spain where Tottenham were embarrassed 5-2 by Atletico Madrid, while Newcastle United held five-time European champions Barcelona to a 1-1 draw in the northeast of England.
Mario Lemina's seventh-minute header secured the win for Galatasaray, who beat Liverpool at the same Rams Park venue in the group stage and stunned Juventus with a 7-5 aggregate victory in the playoffs.
Both sides had goals ruled out after VAR reviews.
"Liverpool is a huge club, full of quality players," Galatasaray manager Okan Buruk said ahead of a trip to Merseyside for next Wednesday's return leg.
"We did what we had to do here. We won. But it's not over."
In Madrid, back-up Tottenham goalkeeper Antonin Kinsky suffered the ignominy of being substituted 17 minutes into his Champions League debut after being at fault for two goals.
The 22-year-old Czech was handed his first start since October — and only his third appearance all season — in a big call by under-pressure Spurs manager Igor Tudor and it couldn't have gone worse.
Inside 15 minutes, Kinsky's miskicks led to Marcos Llorente and Julian Alvarez goals.
Kinsky was immediately replaced by Tudor, with Guglielmo Vicario coming on, and looked inconsolable as he walked down the tunnel at Metropolitano Stadium.
"It's difficult to explain this," Croatian Tudor said.
"We gave away three goals at the start, and then it became very difficult for us.
"He (Kinsky) understands why he (had to) go out ... he was sorry. The team is with him. Me too. I was speaking with him, he understands the moment."
With PA & DPA.
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