This is a terrible start for black in both games. If your aim is to get the final corner, you could play it without approaching komoku at all. You could also ignore his pincer and play the final corner. Another possibility is this well-known joseki for gaining sente:
All of these ways are valid, but the way you played is most definitely not. Also, any cut that can split your one group into two weak groups cannot possibly be called "not big enough for white." So yes, the result in the games truly is terrible for black, not for white. At least you made up for it in the first game with white's bad play at the top
. I haven't looked at either game too closely yet, but don't fool yourself into thinking that your tiny bit of defective influence is worth massive amounts of white influence while white is not sealed in fact is ahead of you in a pushing battle on the third line (on the left in the first game, top in the second game).