Guilty and sad

My boyfriend went to jail because of me on June 18th. I was supposed to meet him at my grandparents house at 8am. I was running late and he didn't want to go into their home without me. He sat on the stairs in the apartment complex and ending up falling asleep. One of the neighbors called the cops on him. When he realized how long he was was sleep (about 45 minutes) he got up to take a walk. The police stopped him and arrested him for loitering. I feel like it's all my faught. He keeps telling me it's not but that doesn't stop me from feeling like it is. I blame myself for him being in jail. How should I feel about this?