해치다 is not the best word, as it means "to harm". it is used when there is a lasting bad consequence. The more commonly used phrase for your sentence is 상하게 하다. 상하다 is an intransitive verb (자동사) meaning "to turn bad or damaged" (이가 상하다 = tooth gets bad, 음식이 상하다 = food spoils) or "to feel hurt/offended" (기분/마음이 상하다 = to feel hurt/bad). 상하게 하다 is often used when you hurt someone's feelings, pride, etc, usually not intentionally. Also, since you don't intentionally hurt your friend's feelings, the present tense form is rarely used. A more likely case would be: 저는 제 친구의 기분/감정을 상하게 했어요 = I (accidentally) hurt my friend's feelings. There are other expressions too, like -에게 (마음의) 상처를 주다 which has a somewhat stronger sense.

It makes sense but this is better 저는 제 친구의 기분을 망쳤어요