라고 느끼다

feel that, in those words

라고 holds a thought exactly as you would think it, and 느끼다 reports feeling it: 혼자라고 느낄 때 "when you feel alone", 사례하고 싶다 라고 느끼는 거다 "you feel like you want to say thank you". The passive 라고 느껴지다 is common and softer — 완벽한 팬이라고 느껴지셨던 적 "a time when they struck you as perfect fans". Keep the quoted part plain and unpolished; the politeness of the sentence lives in 느끼다 at the end.