Depends on what the fuck up is related to. Screwed up something like productivity or efficiency, or wasted some time because I did something wrong administratively and have to redo some paperwork? I don't give a shit. Screwed up something that actively impacts a person, whether through safety, overwork and stress or whatever else? Yeah, then I'm super pissed at myself and concerned about the mistake.
For example, let's say I'm doing some paperwork for someone's promotion and I screw it up and they don't get the promotion. Or I forget to process (or even just get to it slowly because it gets buried in a pile of stuff) an acquisition request for some safety equipment. Yeah, I definitely care that I screwed up, because I have directly harmed someone's well being. That can have a significant impact on their personal life, or for something like safety equipment can literally cause harm to people. But if I screw up the paperwork on a quarterly report, or I run a shitty meeting and my boss gives me a blast of shit? Pfft, I don't care at all, in the grand scheme of things that doesn't matter at all.