"did not + verb" (by itself) only works with intransitive verbs; "verbed + nothing" only works with transitive verbs. So, your question is applicable only to verbs that can be either transitive or intransitive, and in contexts where both forms fit and make sense. Intransitive "feel" (at least, "feel" with no arguments) hardly exists, so I don't think that your example is very viable.
New words, one handy idiom, and a 2-minute quiz — delivered to your inbox to keep your streak alive.