It was the second time Llorente had scored twice at Anfield as Atletico fought back from 2-0 down, but ultimately lost this Champions League tie 3-2.
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Afterwards, Llorente said: "(Virgil) Van Dijk's goal can happen. What can't happen are two goals so soon. That's football. It's the first Champions League match and there's still a long way to go.
"They're a great opponent. They got into us very easily at the start and we have to try to resolve those issues."
On his two goals, Llorente added: "I'm thinking about the three points and winning. Today the two goals were of little use."