This is technology but inside of this, there is no system to warn us "You input wrong currency adrress".
That is because Bitcoin and Bitcoin Cash addresses are completely indistinguishable (Bitcoin Cash copied Bitcoin entirely which includes the address prefixes). There is no way for a system to warn you that you entered the wrong address because both are valid Bitcoin and Bitcoin Cash addresses and there is no distinction between them, i.e. a Bitcoin address is a Bitcoin Cash address and vice versa.
The only thing you can do is to contact Bittrex and see if they can do anything. In theory they can because they control the private key for that address and Bitcoin and Bitcoin Cash private keys share the same identical-ness properties of addresses.