It's not your fault as long as you did your absolute best in the game to support the players who weren't carrying their weight.
The important part about climbing is ranked is that, even though you may not feel like it, everyone gets feeders and players who weigh them down. There's nothing that can be done about getting placed with them. A lot of games are decided in champion select based off of who you're put with/against. Sometimes you'll get the diamond 1 smurf and sometimes you'll get the "diamond 1 smurf." That's an integral flaw to matchmaking and you just need to accept that if you're going to climb.
Unless you can literally 1v5, you aren't going to win every game, nobody is expecting you to. You just need to win more than 50% of games. The only thing you need to do to climb in rank is improve and ensure that you are consistently contributing as much towards a win as you can.
#TLDR: you can't win every game, but you have to do your best every game if you want to win.