well, looking at your 33/7/18 match...
Your composition, for starters, is pretty terrible. Your biggest threat in teamfights is Malphite's ultimate, and you don't really have any hard aoe CC to defend against an engage. So the moment Malphite lands an ult on your Cait & Quinn, you're screwed. Since Teemo has frozen mallet, he can slow your team & prevent cait & quinn from kiting Garen & Blitz (who are obviously rushing them). Your team has nothing to save you guys from that.
Shyvana is great at diving the enemy backline & bursting a squishy carry. But no matter how fed she is, she can't peel for her team & keep them alive. I myself have main'd Shyvana at a point in time and would get so fed I could kill an ADC in 1 Q and 2 Autos. But my team couldn't protect themselves and they'd get slaughtered while I killed 3 of 5 enemies in that teamfight. If you guys had... idk... maokai or galio top for instance instead of a quinn, someone who could act as a frontline and keep Garen or Blitz off of Cait, you could most likely have won. Or if you were a jungler who could peel for your 2 ADCs instead of simply adding extra damage to your composition. Also, remember to let your teammates secure kills too because there's only so much you can do in a 1v5. Even if you do 90% of the work, let them secure it so they can get the kill gold.
I would also analyze your performance but I can't watch the actual match. When you kill someone, do you do anything after? When you kill the enemy jungler, are you IMMEDIATELY invading their jungle and taking their camps? Are you taking herald or a drake knowing you can now safely secure it without risk of them stealing it? In team fights, are you being greedy by trying to ace them? Or are you taking what you can get, backing off, and taking a tower or baron knowing you have a numbers advantage on your side? Everyone in that game died WAY too much, including yourself. It's a little bit insane that the score is 53 v 69 and 50 minutes long. So your team is obviously focusing too much on kills and not enough on objectives. Towers are way more important than kills.