(I guess, too much Tsumegos make you lazy because you expect someone to tell you, Black to "kill" ^^ When you stated you omitted the last move, I only started to look at the positions. But I looked at H4 at first =P)
Don't feel bad for being a kyu player and not spotting it - I looked over a game between two 3ds on KGS from like two years ago and this exact position came up - they played about a dozen 1-point gote moves at the end before they noticed it was seki! Useful position to remember as it is not too rare.
I immediately moved to counting since it was the end of the sgf. I was like, wait, white's just ahead, what's going on? And then I moved my face a foot back from the screen. It was like one of those "Once you see it... you'll s*** bricks."
A year ago I wouldn't have seen the move(s) even with the big clue there are moves to be made. I would have given up and thought I wasn't a 'real' Go player. But now I can see them easily when I'm told. This gives me a warm feeling. Now I need to see it without being told. I wonder how many years until then . . . . And it seems so simple too . . . .
going H1 instead of F4 I think would've gotten it closer to a tie. 2 more points for 2. if you don't like H1, do G1, it also takes away a point from black, but you lose sente doing it not sure why but that seems better.