No reason why going through a major puddle should be problematic - tho you did drown your electrics.
The light could be short-circuit - its obviously connected to the engine at some point and the water might have affected it.
It could also be an engine fault that has decided to manifest itself at that time and is unconnected to the puddle.
Don't ignore warning lights in case you do serious damage to the engine. Check the levels of oil and water and try to think of any obvious reason why the light might appear - recent undue noise, a missed service, a component that you have been told might fail or was due for replacement.
If the engine still runs, it's clearly not a catastropic fault, but might stop the car soon if not attended to, so take the car in to have it looked at.