Each public key (adress that you have) have it's Private key so it's impossible saying that you sent coins to a adress that dosen't have private keys , I don't think it's possible to send coins to Adress that dosen't exists yet . Have you checked any blockchain explorer website to see really if you sent the coins ?
Just for the heads up, it *is* possible to send bitcoins to a wallet you haven't fully set up yet although if you got a public address there must be a private one too (make sure it's saved and backed up asap). Since a simple transaction merely sends coins to a public key *hash* you can even create a public key out of thin air by hashing random data without ever having a private key for it (you'll obviously lose these bitcoins).
On the other hand, a bictoin pubkey uses a special encoding that includes verification data. The goals of the public key encoding are multiple:
1. Shorten the length of the key representation by using letters and digits
2. Avoid look-alike letters (O & 0, I & l...)
3. Avoid typing mistakes by validating key using 4 extra bytes
4. Differentiate between address types
#1 & 2 are done using bitcoin-specific Base58 encoding (similar in spirit to Base64 but using a custom table and without the letters above)
#3 & 4 are done with special algorithm designed specifically for Bitcoin - see
https://en.bitcoin.it/wiki/Base58Check_encoding#Creating_a_Base58Check_stringBecause of all this it is not easy to type random bitcoin addresses in the normal form, however any sha256 hash (and by extension anything 32 bytes) can be transformed into a well-formed bitcoin address.