Baby seems over tired after breastfeeding
Depending upon the age of your baby, that can be normal. For very young babies, breastfeeding, or any feeding, is a very laborious activity--it's one of the hardest things a young baby does all day. It would be very natural for a baby to go back to sleep after feeding for, say, the first two months. After that, babies start to stay up longer.
If you're at a point where you think that your baby should be awake more often, contact your doctor.