The French defender, who already shares a difficult relationship with the German manager, last weekend blamed the club and the manager for lying over his absence from the squad via the social media app.
Surprisingly, Sakho made his first appearance of the season for the Under-23s' Premier League International Cup game against Wolfsburg during mid-week but is unlikely to force his way back into Klopp's first-team plans.
"It is a rule for every player. Work hard and do your best. The rest of this I spoke to the team about and I spoke to Mama and we spoke together and that's it.
"From my side everything is done and now we can carry on. There is nothing else to say."