If you forgot to get something like homework or other things,
you don't have to use "남겼어요".
Because "남겼어요(its basic form 남겨두다 or 남기다 literally means you left or put something at some place). It's close to keep something, which is "뒀어"(not 눴어)
So you can say,
"숙제를 집에 두고 왔어", which means you slipped your mind to get your homework.