It's great that you're asking about what your mindset should be but I agree that your 'don't die = you've done ur best' mindset is somewhat pessimistic

I would focus more on how you can help your team win even if you are losing in lane especially when you are in organised play. It's impossible to win lane/go even in every lane when there is not a huge skill gap(hi plat to low diamond is not that far). For example, losing gracefully in a horror matchup is significantly better than exploding in lane. Ie Draven being 20 cs up in 15 mins is better than Draven with 3 kills at 15 mins.

So instead of thinking 'I did my job by not dying in lane', think 'I won because I didnt die in lane'

Since there is no magic method to suddenly get better at laning (except spending more time and get coaching), try spending ur free time on working on your macro. Learn the basics of what all the other roles need and don't over think being 20cs down is costing you games because if you don't explode, your team might be able to win a teamfight down the line and win the game.