I don't know how to tell people I messed up

So I've lost something that I've been entrusted with (I needed to hold onto something for a friend temporarily) and I just couldn't find it because I couldn't remember where I left it. Sometime last week my friend asked me where it was, and I told them that it must be somewhere at my house because there was no other place it could have been. I looked everywhere and couldn't find it, and I called and checked every place I could've potentially left it at - still haven't found it. Now I've got to tell my friend that I've lost the thing, apologise, and make it up to them, but I just don't know how to tell them.

It's not just in friendships, at work as well - I can never straightaway admit that I messed up, I need to spend time and convince myself to say it now, tell them. I want to take responsibility, but it feels like something's physically stopping me and maybe I feel anxious, but that obviously isn't an excuse to skip apologising.

How do I:

1. Tell my friend that I messed up and apologise for it (what's the most effective and appropriate way to do this)

2. Change myself for the future so I can get better at owning up to my mistakes straight away

The thing that I lost is quite important to the friend, and would impact them a lot.