No, losing your virginity is not supposed to hurt. Pain during sex is never supposed to happen. It happens a lot, but it almost always can be avoided if people just know a little bit about their body.
The number one cause of pain during sex is not enough lubrication. Many girls have sex without knowing when they are lubricated enough, without having enough foreplay, and without buying extra lubrication.
The second most common reason is being nervous and tense. Being tense makes your vagina tighten up. That can make penetration painful.
The third, and least common, reason that sex might hurt is various problems like infections. So if the pain persists even with adequate lubrication and when you are fully relaxed and comfortable, tell your ob-gyn about it.