It's simple, really. Play better. Not your team, you. Trust me when I tell you that it is a lot easier than it sounds!
First and foremost, you have to realize that despite how seriously you take it, League of Legends is just a game. It's not the end of your League career much less the world if you lose a game or two. You can play a perfect game and still lose--so it's clear that the two do not always imply each other.
That being said, do not aim to win the game, but to play well. Know the strengths and weakness of your champion as well as those around you(your team and enemies.) For an easy example of this, if you're
you can use the knock-up created by anything for your ultimate. If you have someone like
or
on your team, you can easily go in for the back-line squishies without relying on your q--or perhaps you can save your q to knock-up any runaways.
That would be game knowledge. A good champ to practice your game knowledge on as opposed to mechanical skill is
because she requires none of the latter and plenty of the former. You should also improve your mechanical skill by practicing your skill shots and combos.
is a champion that is all skill-shots so he makes some nice practice for that particular issue. Apart from that, you'd have to learn the mechanical skills for each champion. This is essentially learning how to farm safely and effectively while maximizing your tradeoffs with the enemy. You could know exactly every button to push, but when it comes down to it, things are a lot more intimidating--variables that you didn't account for arise. You have to adapt.
And that is the single most important piece of advice. Adapt. There is no one build to kill all or one way to use your combos. If as an ADC you are fighting someone with a lot of CC, build a
or an item with tenacity. If you are
mid and fighting a
roll out an AD build to counter his passive. You'll either force him to buy more armor than he needs(and thus he loses out on AP) or shred him.
TL;DR: Improve game knowledge and mechanical skill. Both are essential. Without the second, you can do nothing with the first... and without the first, you can do nothing with the second. Adapt. One key won't open every door, sometimes you gotta try a different one.