If the wound is a superficial wound, does it mean there's nothing to worry about?

Possibly: Superficial wounds can still get infected. Keep it clean, and covered with triple-antibiotic ointment. If it seems to be getting worse, see your doctor.

Less worrisome: Deeper wound means higher chance of injury to important structures such as nerve, tendon/ligament, and bloodvessel etc..Injury to blood vessel is often immediately visible--bleeding excessively. Lack of feeling/sensation suggests nerve injury and unable to move/control body part suggest torn tendon/ligament/muscle. Eye injury needs not be deep to have serious problem. Consult doc. Good luck.