IPA: /ɪnˈsɛn.sɪ.tɪv.li/
KK: /ɪnˈsɛnsɪtɪvli/
In a way that shows a lack of concern for the feelings of others.
He spoke insensitively about her loss, not realizing how much it hurt her.
Insensitively → It is formed from "in-" (meaning not) and "sensitive" (from Latin "sensitivus", meaning capable of feeling or perceiving) and the suffix "-ly" (meaning in a manner). The word "insensitively" means in a manner that is not sensitive or lacking in awareness of others' feelings.
Think of 'not' ('in-') being combined with 'capable of feeling' ('sensitive') — this helps you remember that 'insensitively' means acting without awareness of others' feelings.