I get it when there's failure we always look for someone to put the blame on. Luis played badly no doubt but arsenal as a team where just poor and couldn't match city's determination to win the game. City miss many chances and could have easily scored more goals than the number they scored in the first half.
Not sure if you watched the match but Luis yesterday cost Arsenal the game 99%. City missing chances does not mean they were scored any goals. They "missed" them. Luis' direct blunders meanwhile led to Goals, that's what counts. I don't see how this counts as blame.
Even after Luis recieved the the red card, arsenal game didn't improve irrespective of them been at disadvantage of one man. They would had atleast show so fighting desire but that wasn't seen which resulted to the three instant change.
The point is he got a red card, again, costing Arsenal more. You can't expect Arsenal to have a fighting chance if they are a man down for longer period of second half against Manchester City which was already leading them by two goals at their tuft. All we would expect is much more humiliation for Arsenal.
Even when the players on the field were even as a result of one of city's players getting injured and no room for substitution they (Arsenal) still couldn't get themselves on the scoreboard, which was a poor performance.
Remember Arsenal were also already one man down, probably already fatigued and 2 goals down courtesy of Luis blunders and sending off, and also away from home. If you are an experienced football fan and expected them to be favorites or to play better football at that point then maybe it's probably my first time watching football or not ever having any experience of playing it in my life... am sorry.
Amidst all what I said, am neither a City or an Arsenal fan