The German head coach was an a combative mood after Liverpool's draw with Manchester City.
Following his team's 1-1 draw against last season's treble winners at home, Klopp took a swipe at Southgate for not calling up Joe Gomez to his squads.
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Klopp said: "Joe Gomez. Gareth, honestly??!"
Klopp said: I am not standing here telling Gareth who he should pick.
But you can get one player and have four positions covered. Wonderful."