C172 Pilot reported a runway excursion during landing stopping on the grass area adjacent to the runway. One runway light was detached; no aircraft damage reported; and the aircraft was cleared to taxi to the FBO.

Narrative

I entered the pattern at ZZZ via a Left Base to Runway X (1100ft). During Left Base; I inputted 10 degrees of flaps to slow the aircraft. Turning Left Base to Final; the descent path fell below glide slope. To return to proper altitude; I increased RPMs; and maintained 10 degrees of flaps. By Short Final; my airspeed read 70 kts.; and I was on proper glide slope. As I crossed the threshold of Runway XX; reduced power to idle; and began to flare over the center line; my airspeed remained near 70 kts. The tires bounced on the runway. After the bounce; the aircraft caught a direct crosswind; which pointed the nose towards the right side of the runway; and rolled the aircraft to the right. Prior to the second and final touchdown; I rolled the wings to level. Upon touchdown; I applied immediate brakes; and back pressure to slow the aircraft and to protect the propeller. As the aircraft slowed to a stop; it crossed into the rounded corner of grass that connects Runway XX to Taxiway 1 and came to a full stop. When this occurred; the left landing gear leg hit and detached one runway light. ATC contacted and advised to continue taxi to the FBO. At the FBO; it was determined that there was no damage to the aircraft. To prevent recurrence; I will perform a go-around in the event of high airspeed and/or a misconfiguration on short final. Prior to my next flight; I will practice cross-wind landings with my CFI to review proper rudder and aileron inputs; and will receive dual pattern instruction at ZZZ.