Well in that case, actually mute them so they don't tilt you. In most games I play, people latch onto one person and treat them horribly all game and call out all their mistakes rather than screaming at everyone. The worst thing you can do is engage them back or talk to them, or worst of all, trash talk them back.
Usually the people that say these things and go after everyone on the team are awful players regardless who will feed no matter what. Thats usually why they're so angry - they're awful and are trying to deflect the attention off their own bad plays to someone else.
Sometimes you can carry them, sometimes you can't. Don't try to reason with them, don't try to talk to them. At the first sign of them being dickish (i.e. spamming the "?" ping after a bad play, spamming 'why???' in chat, etc.), simply say 'muted' and move on, and usually these ppl will stop. If not, then you probably need to go up a few divisions where you can't behave that way and maintain your MMR.
But hey, people prob won't read this or will downvote it anyway. Who cares.