No, you can't use water for contact solution. You should never use tap water, bottled water or distilled water as a substitute for contact lens solution.
In fact, you should even be careful about getting water splashed in your eyes when swimming (including swimming in chlorinated swimming pools), soaking in a hot tub, surfing in the ocean or waterskiing or boating on a lake or river.
Dangerous microorganisms, including the parasite that causes Acanthamoeba keratitis, can be found in these environments, and if they adhere to your contact lenses or get trapped under your lenses, they can cause sight-threatening eye infections.
If you do swim or get water splashed in your eyes while wearing contacts, remove your contact lenses as soon as possible, thoroughly rinse the lenses in contact lens solution and store them overnight in the same multipurpose solution to thoroughly disinfect them.
As with all potential eye problems, the best treatment is prevention. If you think it's possible you might find yourself in situations where you won't have access to contact lens solutions, avoid the problem by wearing daily disposable contact lenses instead of reusable contact lenses.
Carry several pairs of daily disposable contacts with you wherever you go, and you'll never have to worry about being without solutions. At the end of the day (or after you get off the beach or out of the pool) simply remove and discard the lenses and replace them with new ones. Nothing could be easier.
For more details, read "Can Contacts Be Stored in Water?"