A winning attitude doesn't come naturally. People are instinctively born kind of scrubby and it takes years of conditioning to remove the various emotions that cripple competitive play.
When I was younger, I was kind of scrubby. I was probably not as susceptible to it compared to most people, mostly because I was better at video games in general and I won most of the time (and when you're winning, nothing you do is cheap). However, little kid me threw tantrums whenever I didn't get my way in games, whether that was playing as P1 in a 2P game or whatever. I grew out of it eventually, I think. Maybe.
It was really concentrated effort that got me really thinking non-scrubby, though. A little over a decade ago, I played Soul Calibur 2 pretty competitively, but I was getting owned by a friend who used lots of guard impacts. I could not figure out how to beat that strategy, and I remember feeling that it was unfair. I didn't say anything though, because I felt like I should be able to just beat it. I was upset, sure.
When I play games with other people, I notice some shared traits. People love to see themselves do well, and they vastly overinflate how well they do. I really like watching pro gamers when they win, and they're like "well we made a ton of mistakes, it was really fortunate that we managed to win." You'll never see that from most gamers. Most people immediately attribute success to their own personal ability.
Average people are not OK with things that damage their own personal self-image. Ask the average gamer about a game he or she likes to play and you will inevitably get the "I'm pretty good at this game." The same is true if you ask someone if he or she is good at anything he or she likes to do. It isn't just games. If a person invests a lot of time and effort ("lot" being a pretty subjective thing) into something, that person will almost universally feel like he or she doesn't suck at it. Of course, when it comes to games this is pretty much universally false. 90% of LoL players are below Gold league skills. The same is true of SC2 players. Over 90% of them average under 50 apm during a game.
The problem is perception. People want to feel good about themselves and aren't good at thinking objectively. If you ever want a really good example of this (and you play LoL so you can appreciate it), watch Nightblue3's stream sometime. He's a really good player and has a good attitude, but he is very self-centric and doesn't think very broadly, often misinterpreting events or what he could have done simply because of his limited perception. Again, this isn't a jab at him; he's a great player and you should watch his stream, but watching him at work can really show you how the "ego goggles" work even for a very humble person.
In order to dump that scrub attitude you have to really look outside yourself and try to see how outside factors contributed to your success or failure, particularly in a team game like LoL. When I play Payday 2 (or really any cooperative game) I am really cognizant of how well my team is doing without me. Sometimes this is because I'm not doing very well and I know it, and other times it's because I am doing well but I know I'm able to do so because my teammates are doing something else that I need to have done. Sometimes I am just carrying my team, too, and because I am more aware when my teammates are doing well and a little more objective about it, I can be more objective when I do pull my team's weight.
One LoL game not that long ago I hit with probably 20 Blitzcrank hooks on players. My team did well too, but I know I was doing well because I can objectively say that I hooked people often, at good times, and with really stellar accuracy that is sort of infrequent for me. I don't normally do that well (that game was hard to top, honestly) and it was easy to see that my performance was both exceptional and vital to my team doing well.
On the other hand, I can't count the times where I've merely been adequate, doing just what I needed to do, occasionally making mistakes or plays but nothing earth-shattering. I have many other games where I've played poorly and won purely by virtue of my team carrying my loser butt. That loss of ego and ability to self-reflect is what's really important to trashing the scrub attitude. If you can objectively assess how you're doing, your pride won't take huge falls when you're doing poorly because you understand that it can happen. You also might know how you can do better later, too.
Some people are extremely self-deprecating, which is a whole different problem. I have met a lot of people who immediately give up on stuff without really trying or putting in effort. "I suck," is the common response. "I'll never get good," is another. "It's too hard," is also very frequent. I only know how to solve the problem from the "dialing down the pride" end. I don't know how to get around the lack of desire to put forth effort. I see people who want to win and play whatever game a lot, but moan about being terrible and never improve. I'd just advise quitting, but if you really want to play and you want to win you need to detach yourself from your failings and concentrate only on doing better the next time.
The most important thing is effort. Try harder! Time is the most important weapon and you can't give up just because you get mad. The most important thing is to realize you're upset and get over it. The problem is that people get too tied up in how well they did and don't work at trying to change.