C-172 pilot reported runway excursion during landing rollout.

Narrative

I was conducting a cross-country flight to ZZZ. The expected runway was XX with winds being 140 degrees at 10 knots. I set up my final approach for XX. Through descent I was on the proper glide scope per PAPI showing 2 white/2 red. The aircraft was configured for low-wing cross wind landing where I had applied right rudder to align with runway and left aileron to keep left wing lower. As I crossed the threshold; I begin reducing more power as runway was made. About a foot or two above the 1;000-foot marker; I did not have enough left aileron correction in which caused the left wing to raise and left main to touchdown first. This resulted in my direction going towards the right and hitting a runway light. At this point; my focus was on regaining control for the situation and avoiding damage to the wings and prop. All throttle had been removed to idle and I allowed plane to slow itself down with wings level in middle grass area instead of applying brakes. After this; I taxied to nearest parking area in front of north hangar to inspect aircraft.After parking; I powered down and walked around aircraft. I could see where light hit the lower left part of cowling (left being when you are looking from front). No damage was observed anywhere beyond that area. Next; I called my flying club board members to report the incident and called the Airport Operations. The Airport Manager indicated the lights were designed with a hinging system to give way like they did. He recovered the broken light and inspected runway. As to my perspective/insights... I knew flying into ZZZ there would be a strong cross wind. However; I had been flying in these situations regularly with my CFI doing instrument training and they were fine. I felt this would be within my capability and was aware of the extra inputs required.My approach was stable and lined up as expected. I believe my mistake occurred when I was about to touch down and had the runway made. I was removing power when the left wing started to raise. At this point; I did not put in enough left aileron to counteract the cross wind.