it's very bad. so don't be silly and stop putting water in your eyes. Water alone is irritating to the eye. Tears are composed of water and salt, however you cannot put saline into your eyes as well, because is not in the right proportion.Ordinary water contains parasites and bacteria which is very likely to cause serious infection of your eyes. If your eyes feel tired and sore, try artificial tears from the drugstore. Better yet, have an eye exam to find out why your eyes are sore. The water you get out of your pipes are chemically treated to make it safe to bath and drink and cook, but your eyes are so much more sensitive then your skin or stomach.So do not ever put water in your eyes.
Yes, it would not be wise for you to let water in your eyes. As you can see, tap water is not properly disinfected and cleaned, therefore, it contains some micro livings and bacteria which would give rise to some thing like red eyes and infections. Also, direct contact with water would make your eyes feel uncomfortable. So, you had better close your eyes when washing your face.
It is not so serious, but you must be careful in your daily life. You must close your eyes when washing face. Canthus can be washed separately. People face is the second dirty part only to hand. though that the tears have disinfection function,
face water can never be infiltered into your eyes.