Look at your bedding when you get up in the morning. Are the blankets all disheveled and twisted around, or pillow knocked to the floor? If you see anything like that, it would indicate you're doing a lot of tossing and turning in your sleep, which disrupts your restful sleep even if you don't wake up. Also pay attention to the temperature in your bedroom. If you're getting overheated at night, that can also disrupt your sleep. And when you wake up, if your sinuses are packed to the rafters so you have to blow your nose a lot first thing in the morning, that sort of blockage can disrupt your sleep by interfering with your ability to comfortably breathe.
After looking at everything and trying different things when you sleep, if you still can't sleep well and wake up feeling rested, talk with your doctor.