Came Out and Feel Weird

An unfortunate series of events have lead me to have to come out to my parents. While they were accepting as they could be, I still feel weird and I can't help but feel I let them down. I attempted to drink the thoughts away that didn't work. I feel alienated from my parents even though they said they loved me regardless of who I marry or fall in love with but I still feel like I've disappointed them. Kind of weird because most people talk about their parents making the situation awkward but to be honest, I feel like it's me making this weird. I don't know if I can look them in the eye again. I don't know how to handle this.