This is the mindset I go into ranked games with. If I lose a game then I need to look at what I need to do better. Of course some games are uncarriable by anyone non-psychic and non-perfect, but keeping this mentality soothes any kind of rage I had for this game. If mid and jungle died to a countergank while I was top, I should have headed down there to help out/clean up. If the enemy mid roamed top and got a kill without a response, I should have been more vigilant with pings/mias/counterganking.
If you play every game with the mentality "I will only lose if I fail to carry my team, and that's MY responsibility", ranked becomes more fun and your ELO will rise much faster
It's never my team's fault, it's my fault. Raging at them will get me nowhere. I need to get better so I can carry harder, and that's the end of it.
EDIT: For the people that think carrying is 1 man army, that's absolutely ridiculous. Carrying means making plays around your map, getting the best environment for your team to succeed, snowballing, and making the right calls. If they ran into a bush and got ganked, I should have warded better, etc
EDIT 2: Score isn't everything. 6/0/0 can mean you only snowballed your lane, 2/2/7 can mean you snowballed other lanes and the team as a whole is stronger
I played over a thousand ranked games in S2, from as low as 600 Elo. I improved a lot, and learned a lot. However, all this is within the cesspool that is low Elo ranked. To be sure, carrying yourself out is the only way to do it, and that means focusing on your own gameplay and not that of your teammates. The problem is, unless your true Elo is plat and you can literally stomp game after game after game, you WILL run into problems. You will jungle with all 3 lanes failing and feeding miserably and have to throw your hands up and move on. You will play mid, being unlucky enough to go against one of the only other people at your Elo who's actually proficient at laning and can counter you. Or you'll do great all game and make one small mistake in a teamfight that costs your team the game. Some of these are completely your fault. Some of them are completely your teammates' fault (because, let's face it, not every - single - game is carryable unless you are plat/diamond and even there...). In a nutshell, solo queue is a roller coaster. You get better, and in turn gain Elo, by focusing on your own gameplay and working to improve it.
But with the attitude that you can always win by carrying harder, you will just burn yourself out. How do I know this? I adopted that attitude for a while. Somewhere in the 900s, when I played regularly with friends who were 1200+ but I myself was stuck way down in hell, I began to tell myself that I could win every single game through carrying. Sounds good, right? It's good only until you lose. And that's when you hate on yourself. You'll wonder why you can't carry noobs, and then you'll start killing yourself over every last detail. It quickly becomes counterproductive. In an unpleasant environment - which characterizes many if not most games below gold - you can only play this way for so long. Pretty soon it just won't be worth it and you'll be pulling your hair out.
There's a different way of looking at it that I think is much healthier, while still retaining the focus on self-improvement. That is to keep a percentage in mind-- just about how often you'd like to win, or think you can win, playing your best. 60% is a good number to start. Play your best, always play to improve, but don't absolutely destroy yourself by thinking that every.single.game must be carried and if you can't do it, well, you suck. Shoot to win as many as you can, not every single one. I have found this to be much better in the long run. This way, you can have a box in your mind - the "40% box" or the "30% box", of games that just don't work out. You still try to learn from them, but it's always expected that you'll take a step back somewhere along the way. For people who are struggling, I actually think this is much healthier and a better way to go than OP's suggestion.
Tl;Dr-- I like where you're doing with this, but instead of soothing rage as you say, I think for most people this mindset leads very quickly to high amounts of frustration and self-blame.