When it comes to self-improvement, there's always one persistent obstacle that will always stand in your way: yourself. The unfortunate reality is that the human brain is amazing at justifying its own actions in hindsight, regardless of whether or not you were in the right or not. That manifests in a very obvious fashion in League of Legends. We've all thought at some point that we did great in a game and would have been able to carry it if that other player just hadn't messed up.
Whoever said that men were more prone to seeing the splinter in the eye of another man then they were to noticing the plank sticking out of their own was wise indeed.
One of the best strategies that you can adopt in League, then, is to try to evaluate your play as if you were watching someone else. For most of us, this is pretty hard to do in game. It requires a cold and analytical mind to discern plays logically while in the heat of battle, and not everyone has that. Emotions come easily to us in the heat of the moment, and those are rarely helpful if you're looking to improve.
The best technique to circumvent that is also a quite simple one: watch yourself play after the fact. For most of us, the difficulty with coldly analyzing our own play while we're in-game is that it requires two level of parallel thought: you have to think both about what you're doing and whether that's the right thing at the same time. In some situations, that works just fine. Jungle pathing can often be improved or discerned on the fly since it doesn't usually take all that much brain power to slaughter the jungle minions, and the free space can be used to plan your path quite easily. Trying to figure out if flashing into a teamfight to unleash a bit ultimate is the right play or not is a much different question, however, since your mind is usually focused just on making the play, not on whether or not that play makes sense. Even professional players struggle with analyzing their own play on the fly, so it's certainly not something to be ashamed of.
Fortunately, reviewing your own replays is now easier than it's ever been. Replays are now stored directly on the client and can be easily reviewed at any time, at least supposing a patch change hasn't yet hit since you played the game in question. Other applications also make this even easier, and there's a reason Plays.tv has become so popular with streamers and professional players over the course of the last year or two. It's not solely due to its ability to upload big plays. It also happens to be a convenient platform to review your own plays. There's plenty of similar programs also on the market, so there's little excuse not to pick up one of these relatively unintrusive programs for the purposes of reviewing your own games. You'll quickly notice the difference if you do.