I have a few tips for you!
First of all: Nobody likes to give their foes an easy win, and that is especially true in LoL. So if your game only lasts 17 minutes (ARAM/Twisted Treeline/Dominion don't follow this rule), it is natural you are at least, angry. Angry that you didn't do your best, angry that the foe simply outplayed you and turned the game into a one-sided match very early, or even the fact that 1 afk cost you jungle buffs or early towers. Doesn't matter. The longer it takes to win/lose makes the victory sweeter, and the defeat less bitter. And the shorter the game is, contradicts this law. It isn't hard to know when a game is lost early: a tower down way before 10 minutes, 10 kills ahead without any chance of fighting anyone back in their lanes, real difference between enemy CS and yours, easy dragons, etc... What is hard, is to not surrender. You know, when two of your teamates refuse to give up, even after everyone getting aced in every single attempt at combat. That, is where the frustration begins. You want to end the game, to start a new one, and try to win that one, instead of wasting your time with one in which you will only be the punching bag, walking around your defenseless inhibitor like a headless chicken, until the enemy decides to put your team out of its misery.
A tip for these situations: try to reason with your teamates. Don't flame. /all omg report my team no surr feeders gg. That never helps. Try to tell them: look, they have 40000k more gold than us, two barons, we have 10 players less than them, our turrets started attacking our nexus, and their caster minions can almost 1-shot us because they evolved into Veigar. It is time to surrender, mate, so we can get to a new game and try to shine in that one :) . Do this (with less exaggerations, of course), and carry on with your life. If they don't surrender, don't be a baby and AFK. Its bad enough to lose without being reported. Try to farm. Killing minions still counts to your overall score, you might as well add up.
Another thing I hate about losing. There will always be that guy: gg ez game. It might last 40 minutes, but when someone says this I always get angry (sue me, I like to think I am decent), and end up reporting them, even if they are in my team. This makes you feel like your efforts were in vain, for a split second, until you join a queue again, but the frustration becomes sharpened by these idiots.
But I have a solution for this as well. These players are easily noticeable by their behavior. If a Tryndamere who spins over a wall, and escapes, screams in all chat: lol try harder nubs not even close bby! then it is very likely that he will not act very friendly towards you if he explodes your nexus. If the enemy Teemo/Lux keeps spamming his/her laugh in lane, then yeah, they might not be the healthiest players. Anyone who calls you lucky or complains about lag after getting outplayed is also likely to do this. If, on the other hand, there is a Sona that, after a teamfight in which she dies due to a mistake she made, she says in all chat: aww, fail flash >.< :3, then yes, she might not be an actual l2win kind of person. Anyway, players that don't show a good attitude towards their foes, are very likely to show an even less good attitude to them, when they win. Therefor, if you notice any of these Tryndameres, Teemos, or Luxes coming anywhere close to acing your team, destroying an inhibitor, or winning, mute them. This reduces the odds of those stupid four letters showing up as the big DEFEAT is slammed on your screen. You can always mute all your foes when you feel like a defeat is near, to avoid trouble.
ANOTHER PRO TIP! You can always do the dance test! I will explain! This is a test that involves standing near your foe in lane (preferrably before minions arrive), and start dancing (Voli dance is love, Voli dance is life). Note: In kill lanes with Blitz/Thresh/Nami/Morgana, etc... it might not be a good idea, so be aware of your opponents. Then, there are two types of reactions. They either fire skillshots at you, or they will start dancing too. I have noticed most players who use skill shots instead of dancing are more interested in winning overall, than in the fun of the game itself. Therefore, their attitudes might be a lot worse than those of players who are calm enough to dance with foes that they don't hate. This test isn't failure proof, but I have found cool Shyvanas that danced with the Volimoves, and scumbag Lees that dashed on me the moment Voli started jammin' the moves, and it works fine most of the time.
Now you might say (about my tip before the dance strategy): but even if I mute the emote spammers, the try hards, the Tryndameres and the luckers, I will still have to put up with the end game screen comments. Well... to that my friend, I have a simple solution! All you need to do is skip waiting for stats! Your response? But that way I won't see anyone's stats! But I say: Not anymore! Thanks to the Match History Beta, you can now see everyone's CS, wards placed, kills, assists, multikills, true dmg dealt, WITHOUT the annoying comments. Removing the gg ez from the game has never been simpler! Enjoy.
But now, lets talk about those wins that consume a really long time. 50 minute games. Those that were really close. If you realize your opponents aren't total kids, you might even congratulate them, who knows? If you are capable of triggering a sense of good sportsmanship in the mind of the enemy victor, he might as well give positive feedback about your playstyle, and nothing feels better than getting your ass kissed. :P It is better to not remain salty and get a complement afterwards, making the game's effort kind of worth it, despite the defeat, than to be grudgy and remaining moody, after a loss that was potentially very, very close, and could have lead you to even getting a honorable opponent badge (or whatever those things are called). If a complement doesn't feel like enough, remember, longer games=more IP, so the more even your games are, the closer you get to that next 6300 champion/rune page, even if you lose. Keep this in mind after a game that took the enemy 30 minutes or more to win.
I hope I made League somewhat better to you. Good luck in the fields, friend!