Separation anxiety

My 1 year old seems to have major separation anxiety when it comes to me leaving to another room. Even when he's with his father he cries to always be near me. I'm a stay at home mom so I'm with him 24/7 everyday. I know I should be grateful that my baby wants to be with me but I feel bad that he doesn't even want to be with his father sometimes. It does also get a little frustrating when I'm doing something or leave for something like groceries & have him crying continuously until I come home or am near him.