I'm sure someone who is better than I am with grammar can tell you why, but that sentence is correct. It was a common saying in English for a long time. It's not as common now, except among older generations.

It was strange of him to act so out of character. It is kind of you to ask. It was presumptive of me to expect you to understand. (Oops. Just kidding.) Yes, you can take this structure and run with it.

"I think a adjective connects to a preposition is wrong." I've never heard of this rule before, and I can find many examples which show the opposite (as other members have done already). "How careless of me!" is perfectly natural in English, and a common construction.

I can't exactly tell you the grammar of that phrase. But it is a very common set phrase. You can also use other adjectives. "How rude of me!", "How inconsiderate of me!", "How wrong of me to...", etc.