The quick answer to your question is that you should use a past simple tense with 'A few days ago'. When you specify the point in time when something happened, you cannot use a present perfect.
There are a few other problems, though. One is your use of the word 'miss', which doesn't make sense here. The word 'lose' is possible, though. We often use this verb for an experience when a person or animal close to you dies. I'll correct your whole post, and then you can tell me if this is what you meant to say:
A few days ago, one of my pigeons died .
Now I want to tell my friend about it. How should I say this?
'A few days ago, I lost my pigeon', or 'A few days ago, I have lost my pigeon' ?
You have two options:
Past simple : 'A few days ago, I lost my pigeon.'
This is telling us about an event in the past.
Present Perfect: 'Why are you sad?' 'I've lost my pigeon'.
This is telling us about the present situation. You're sad because no longer have one of your pigeons. If you don't specify when the pigeon died, it's possible to use the present perfect. If you do specify the time - 'a few days ago' - you have to use the past simple.
I hope that helps.