The only way to tell if you cut needs stitches is for it to be evaluated by a qualified physician. From the description you have provided, it sounds like you very well may need stitches. Injuries that involve sharp objects such as a recently opened can of soup produce lacerations. This is clean, sometimes deep cut that breaks through the skin. Lacerations are treated differently depending on their depth, length, location, and involvement of important structures beneath the skin. Failure to treat such a cut appropriately can result in infection, prolonged time to heal, and excessive scaring. It is for these reasons that you should not let this go. Even if you don't need stitches, the wound needs the appropriate care. In addition, you need to make sure that you are up to date on your tetanus shot.
I suggest that you schedule a same day appointment with your primary care physician
. If you can't get into to see your doctor
, then I suggest that you go to to the emergency department or urgent care at your local hospital. Your window of time to get stitches after a cut is only 24 hours. After that, stitches cannot be placed, and the wound will have to heal without them. Good luck.