When a friend asks if you want to go to dinner, but have already eaten, then you say "もう食べた".
Is there a way of saying "just ate" (a few minutes ago). Maybe it is another way of saying もう食べた
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I would say
This literally means "I just ate".
I think it's a little more neutral than 食べたばかり（だ・です）.
ばかり feels more like "I can't/won't eat any more" where ところ feels more like "I just had dinner".
済ませました、済ませてしまいました: This phrase is a little polite.
もう食べちゃった ： This phrase is very frank,usually used it to friends or family.