We do use verbs of sensation like “feel”, “see” & “hear” with a bare infinitive. I believe this is one of those cases. The main verb is of course “felt” in the sentence; “take” is the infinitive without the “to”. Another example would be “I saw the thief drive off.”
More often they are used with the present participles: “I saw the thief driving off.” “I felt my father taking my hand...”
It might be instructive if you would ask the students to change the sentence from a simple past to a complex one with the noun clause like “I felt that my father took my hand..."