The soon-to-be-experienced consequences of my not having done the task are more significant than the fact that yesterday I did not do/forgot to do my homework. This use of the present perfect is very appropriate when I get to school and admit to the teacher what the present state of affairs is: I haven't done my homework, and I know there are going to be consequences (the teacher is going to admonish or punish me in some way). At school the next day, the forgetting is in the past, so I use the simple past tense. At that moment, there was still the possibility of my sitting down again and doing that piece of homework, and that's why it would have been natural to have used the present perfect.

If I had noticed that, late last night, as I was putting my books away, I might have said to myself 'Oh, no! I've forgotten to do my English homework. I forgot (at the appropriate time, probably yesterday evening) to do my homework.

If you forgot the work at school, see if one of your classmates knows the. I'm not sure why this should be, so let's examine the two sentences. If you forgot your work at home, see if a parent can bring it to school and leave it in the office for you.

The present perfect is fine in (3), but not quite so good in (2).

I forgot my homework at home