Grammatically, either version is fine for OP's context, but most people would probably go for the shorter Simple Past version most of the time (if only because it is shorter and simpler).
The difference is really one of fine nuance. Present Perfect focuses more explicitly on your current state - that of being without your wallet due to (past) forgetfulness. Simple Past actually carries the same meaning in OP's exact context, but it's important to note that this is a contextual implication.
Consider a slightly different scenario where the speaker is paying his drinks bill with a credit card, but forgetfulness strikes in the form of a senior moment at the "Enter PIN number" stage. Credible things he might say to the barman to explain the problem include...
1) I have (more commonly, I've) forgotten my PIN
2) I forgot my PIN
3) I forget my PIN
I think in that situation the Present Perfect would probably be most likely. Note that in practice the Simple Present (#3) doesn't actually occur very often with the specific verb to forget. We don't tend to think of forgetting as a "continuous" activity - it's usually the case that at some unspecified point in the (usually, very recent) past the speaker realised he couldn't recall some relevant information because it had already been forgotten. Thus to some people it might sound a little odd to use Present Tense to say you're currently forgetting something - which almost implies that immediately prior to speaking, you hadn't yet forgotten it.
Short Answer:
Both are perfectly natural, and it would be stretching a point to say either is "better" in most contexts. But as ever - for simplicity, most learners would do better to avoid Perfect forms unless they're absolutely necessary (the KISS principle).
It is easy to find a context for that sentence. The idea is that verbs in Present Perfect tell us something about the present, and verbs in Past Simple tell us something about the past.
'Never' doesn't necessarily trigger the use of Present Perfect, because it can refer to the past and future, too, like in "I will never marry you!"
As for the 'never' in a past tense, just imagine that someone tells you about things that are gone, that are not connected with the present. For example, Jack tells about his childhood:
As a child, I never saw this movie, although it was quite famous then. Only last year I saw it for the first time.
Best Answer
The simple past did is used about something that was completed at some point in the past.
The present perfect have done is used about something that started some time ago and is still happening, or was completed some time ago but has a lasting effect.
In your example with did/have done, both are OK and there is not much difference between them. You might be more likely to use did if you are talking about a single action in the past and have done if the activity took some time extending until now, and/or it is expected to continue.
The difference is more noticable with a word like work:
and reserve