Gomez and ex-Liverpool star Sterling were involved in a scuffle at St George’s Park on November 11, the day after the pair clashed in the Reds’ 3-1 win over Manchester City.
Southgate dropped Sterling for England’s 7-0 win over Montenegro, a match in which Joe Gomez came on and was booed by certain sections of the crowd.
Sterling returned in the 4-0 victory over Kosovo as England wrapped up their Euro 2020 qualifying campaign, though Gomez - who has insisted the matter has been fully put to bed - missed out with a knee injury.
Klopp expects Gomez to be able to play against Crystal Palace on Saturday if required, and the Liverpool boss is satisfied with how Southgate dealt with the situation.
“Gomez is better than good, everything is fine,” Klopp told a news conference on Friday.
“If people are not sensible with it, it gets made bigger than it is and we speak about it for five weeks. The people involved are fine.
“Things like this happen in a football environment. It’s a big challenge to ask the boys to give everything against each other and then the next day ask them to play together.
“There is nothing more to say about it. Gareth and the English FA dealt with it like I think it was right, I cannot judge because I was not in the situation. Joe is absolutely okay, nothing else to say about it really.”
Liverpool’s triumph over City at Anfield sent the Reds nine points clear of the defending champions with 12 games played.
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