How to Say "deeply felt" in Spanish
The Spanish word for “deeply felt” is “sentidos” — B1 level.

Examples
Los chicos fueron muy sentidos al disculparse por el error.
The boys were very sensible/sincere when apologizing for the mistake.
Sus agradecimientos fueron muy sentidos; podías notar su emoción.
Their thanks were deeply felt; you could notice their emotion.
Siempre actúan de forma sensata y con sentidos propósitos.
They always act sensibly and with prudent intentions.
Agreement is Key
When 'sentidos' is used as an adjective, it must match the thing it describes. Since this form is masculine plural, it describes masculine plural nouns (e.g., 'propósitos sentidos').
Confusing Noun and Adjective
Mistake: “Using 'sientos' (a non-existent word) instead of 'sentidos' for senses.”
Correction: Always use 'los sentidos' for the five physical senses.
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