Named man-of-the-match, Kvaratskhelia scored in the 2-0 quarterfinal first-leg win on Wednesday night, though believed the hosts could've scored more.
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The Georgia international said afterwards: "I think we had the opportunities to score more. We should have scored more goals.
"But I think it's good, we had a good match, we're going to play at Anfield, in an incredible atmosphere.
"We are ready and we will prepare today for this return match."
Kvara also mentioned his compatriot Giorgi Mamardashvili, who was in goal for Liverpool.
"In the first half he made an incredible save. We are very good friends, I wish him the best," he concluded.