You failed to remedy the issue. Upon noticing the spilled coffee, you should have:
A. Stated "Fuck you, too, coffee!", then proceeded to throw the remainder out onto the ground, or
B. Realized you weren't awake enough to not be drinking the coffee and, thusly consumed the remainder posthaste, with little disregard to any overspill. After all, coffee was everywhere anyway, who would've noticed?

You say the problem was the lid being open, but that was only a minor detail. The real problem was that you decided to carry around coffee that you had no intention in drinking.