Learn from the deaths.
How do you think people learned that akali isn't as strong as riven until at least lvl 6? It is because they go hard when they first start playing the new champ, and understand that they died possibly because they either misplayed, or simply because their champion isn't as strong in the matchup as the opponent.
Thinking this way helps you understand eventually what levels, or as some say, where your power spikes are for certain champions. It also helps you understand when you can use these power spikes to your advantage.
Once you learn when you are stronger, it then becomes how you can get those power spikes. Pushing allows you to get levels before the enemy because their minions die first. This is common for riven as she can all in someone if she is lvl 2 and they are lvl 1.
Other times you have to allow the enemy to push. This can occur when you are playing someone that even if you gain a level advantage, say lvl 7 vs lvl 6, they can still win the duel in lane.
So in other words, feeding may piss off your team in the short term, but will allow you to learn more and therefore get better faster then anyone else around you.
On a new Champion never play like a wuss!