Wow. Pretty bad memories.
Worst cases of chess blindness
I made similar mistakes after hard training and reading a bunch of strategic and tactical books. My knowledge grew up a lot, but I began to make terrible blunders...

The odd thing is, it wasn't a case of not paying attention, but more like overcalculation.
I overcaculate too sometimes in blitz. In tournament games too.

The odd thing is, it wasn't a case of not paying attention, but more like overcalculation.
I probably wouldn't have seen that these moves are checkmates if the pieces hadn't stood there. But overlooking that pieces are hanging and doing absolutely nothing about that sure is a weird sight.
What kind of "calculation" can lead to this. It doesn't even look like the moves you did instead fulfill any purpose whatsoever.

It's not true. The moves do fulfill a purpose - but they are just too slow about it.
In the first example, Na3 develops a piece and almost protects the Re1, as one would only need to get the Bc1 out after that
In the second example, b3 almost gets the Bc1 out - just one more tempo was needed...
Incidentally I think that he's already lost after ...Qc7. The only move after ...Nxe5, if I see correctly, would have been Qh3, where ...Qc7 could be answered by castling, and still black has a big advantage despite dropping h8.
It happens to everyone. I recently had a nice attack going and I missed an obvious mate in one by my opponent. D'OH!

You can sometimes get so involved in a position, you simply forget the obvious. I have had it happen to me, ( more than once, and not just in chess either). I also know it can happen to others as well, even GM's can have this happen. So don't feel alone. Good luck, and hopefully don't forget to always take that final look around, to make sure you aren't overlooking the obvious.
In this quads tournament from about 2 years ago I was rated about 1900...and I can't explain what happened. Look at these 2 games!!