Think of your recently-pregnant uterus as having an open wound - the area where the placenta was attached is like a giant internal wound that needs to heal (picture ripping a scab from a burn on your skin). It takes longer to heal since it's inside, and longer still if you overdo activity after childbirth, as many new mothers do.
Pieces of the placenta left behind would quickly turn septic, the placenta should be all gone during the third stage of labor, shortly after birth, when it's expelled. The midwife or ob should have checked the expelled placenta to make sure it was complete.
If you feel generally ok, no fever , chills, etc, it's probably not retained placenta.
The uterus does not just "fall apart". As it contracts back to the pre-pregnant size, the extra dead tissue has nowhere to go and it gets expelled. Again, it's a wound, healing from within. Don't panic.