Was it Okay for me to Do it this way?

So I broke up with my ex awhile back but when I did I told him some really ugly things when I found out he lied to me-it's personal. When I found out it was so shocking it felt like whiplash-it hurt a lot. I called him a liar, told him he lied to me, to stay away from, said he was unfaithful and that was why he talked to other girls(his ex was always interefering in our relationship & he would go along with it) and I didn't even want him anymore after what he did. I was very hurt about how he lied (something he hid from me the whole 8 months we were together & he knew how I felt about it) but several weeks later I did apologize to him & told him I was sorry for getting so sad & hurt. He said he was sorry for making me sad & we nvr spoke again. was I wrong the way I handled it?