I was pushed to submit a mediocre paper to a conference. To my surprise it was accepted. How to save face?

How to save face? Have more high quality papers than poor ones. People understand that a student's first paper is not necessarily outstanding, especially if his/her supervisor is more about quantity than quality. So it reflects more badly on your supervisor than you as long as you have the 'student' badge on. However, you can only wear the 'student' badge for so long. So, aim to get better papers published.

Personally, when I glance at a person's CV, I only look for the best publications. That's what I judge him/her on.

In summary, people remember successes or high quality papers or those with impact.

Aside: in my area, there is a paper in a poor venue with 10K+ cites. In contrast, lots of high quality papers have zero citation. Don't despair, there is hope!

I feel the first step is to calm down and to stop exaggerating. Seeing this as an "evil mistake" and a "predicament" that's "embarrassing" is really, really over the top for just having published a paper that's correct but uninteresting at a low-competition conference from a reputable publisher. As you say yourself - "when the time is ripe" you will start publishing better papers, and then nobody (including you) will care anymore about this weak one. And before that time you have at least gotten some experience in writing papers.

Now to answer your actual question:

How to distance me from this evil mistake hanging in IEEE Xplore with my name on it forever.

The only way to "distance yourself" from a paper is to retract it, and that's not really an option given that the results are not wrong. That is, you or one of your co-authors have submitted this paper under your name, and now you need to live with it. However, note that it "hanging in IEEE Xplore with your name" is much less of a big deal than you may think it is. The internet is a big place, and a paper in a small, non-competitive conference is virtually invisible as long as it does not get cited frequently or otherwise gets viral (which, if it is boring as you say, is very unlikely to happen).

Your supervisor, who has more experience than you, thought that the paper was worth publishing. The conference programme committee, who are all more experienced than you, thought that the paper was worth publishing.

You should give serious consideration to the possibility that they actually have a better idea of your paper's worth than you do. It is very common for research students to feel that their papers are of little value.

And even if you're right about the quality of the paper, one mediocre paper really isn't a big deal. A pattern of mediocre papers is... well, mediocre. But you surely get more credit for a single mediocre paper than you would for no paper at all. Make sure you feel the next one is better.