I took the first address that I have ever used with this wallet and it seems I found the private key.
Before I sent all my funds to another account and now i tried to import my privatekey to Coinomi wallet.
Unfortunately I receive this message: "The private key does not contain any funds"
I am somehow clueless, what did I do wrong ? And how can I redeem my funds ?

I know exactly what you are talking about. A wallet contains many addresses. (That is why the term "wallet address" is wrong.) Unfortunately, I haven't used Bitcoin Core in a long time so I don't remember how to get the addresses with bitcoin coins in them. Take a look at the debug commands to see if there is an appropriate one.