bad, badly

Bad or bad means not good. Bad modifies ( describes ) a person, place, thing, state, condition, or idea--
"One bad apple doesn't spoil the whole bunch..."
This is a bad location for a new store.
He's in a bad situation.
That's a bad idea.
Don't feel bad; you couldn't help it.

Badly or badly also means not good, or not well. Badly modifies ( describes ) an action--
He plays tennis badly.
She sings badly, but she seems to enjoy herself.

Now that you know that, you can say--
"He feels bad that he played so badly."

Note--to feel bad would mean to feel sick, hurt, or upset; physically or mentally bad--
You should call the doctor if you feel that bad.
He feels bad that he hurt your feelings.
Note # 2--to feel badly would mean to do a bad job of feeling something--
He feels badly; he said that sandpaper is soft.