Tracking transactions in both directions I have an example of a transaction. I deleted some fields which don't play any role for my question. Also I reduced large hashes and IDs.

{
 "txid": "8d554",
  "vin": [
    {
      "txid": "d3117",
      "vout": 0
    }
  ],
  "vout": [
    {
      "value": 1.99995000,"address":"mrL8SS",
      "n": 0
    }, 
    {
      "value": 3.00000000, "address":"mtK8r",
      "n": 1
    }
  ]
}


From this transaction I can find out which transaction was used for paying outputs of this transaction. Because those transaction is in vin field. Its txID is d3117. So if I want i will be able to find this transaction by using bitcoin client RPC API: bitcoin-cli gettransaction d3117. 
  But what if i want to find out, which transaction used THIS transaction as input? Could you guys please tell me, if it's possible or not?
That's not possible without looking through all the transactions after this one and finding the one which spent it. Most block explorers keep a database of the transactions so you could look it up on one of them.