C172 reported a runway excursion during landing; citing inadequate crosswind correction control inputs as contributing.

Narrative

Attempted to perform a short field landing in a crosswind on Runway XX of ZZZ. I believe the aircraft was not corrected enough for the crosswind; and was still crabbed into the wind when touching down. After touching down; the aircraft started moving off to the left of the runway; and directional control of the aircraft was lost due to slow approach speeds and crosswind causing the aircraft to weathervane into the left crosswind. The aircraft left the runway and continued to the left of the runway until hitting some mud off the side of the runway. Right rudder was used; but it was not effective. Flaps were raised to aid the brakes. I don't fully remember the incident; it happened quickly (I had lost directional control in 2-3 seconds.) The best I can figure; I landed in a too-high crosswind for the flap setting without enough corrective crosswind inputs. This could be due to me being tired; as I had been flying most of the day; but also a poor understanding and respect of aircraft crosswind limitations.