It was at that moment that my father's criticism cut me to the quick.
Literal
Father's criticism [subject-が] my heart [in-に] keenly was-felt [nominalizer-の] [topic-は] that-time was.
A cleft sentence: ~のは...だった ('it was [time] that [X happened]'). 痛切に感じられた combines 痛切 ('keen/acute') with the passive/spontaneous 感じられる ('was felt'). This structure is a powerful way to emphasize when something occurred.