Klopp took particular aim at Gomez after his team conceded twice in the second half from defensive lapses.
He was unhappy at the defender shooting from 25 yards out at one stage, rather than passing to open teammates.
Post-game, captain Virgil van Dijk told TNT Sports: "Defeat, obviously it is half-time and we're 3-0 down which is not great.
Too many individual mistakes and we got punished for it. I think with the man marking system they do we have to do much better, keep the ball longer, they won all the 50-50s and the spaces were too open.
"It is a very disappointing night for us but we can't dwell on it for too long because we have another game in two days." The defender added: "If we don't have belief there's no point going there (to Italy)."