Guilty of grammatical errors, as charged
Hesitant though I am to disagree with Review Editor Emerita Cathy Perkins, I think the issue is that "feel,” in these cases, is more a to-be verb and requires an adjective rather than an adverb. I remember reading in something quite authoritative that "feel bad" was correct and have used that ever since, even though it sounds wrong because most say "feel badly."
By the way, the Review editor used the phrase "a lot of people" in his comment. That is definitely incorrect!
"A lot" is for bulk nouns like snow, sugar, oil, etc ."Many" is correct for countable things like people, rocks, cars, etc.
Sandra McCrudden Black, Arts’58