Actually, you went 9/2/10, and had a 54% contribution/kill (Meaning you tied with Corki and Janna had a higher c/kill than you). Corki and Zed both seemed to be doing pretty damn well, all things told (Corki 11/7/8 and Zed 10/11/7). The other team almost universally outfarmed you guys. You took the first dragon while your first twoer was falling, and by the time you guys got a tower, two more towers had fallen. They outscaled you in gold the whole game.
It looks like you guys just kinda let Yi split push. You were killing brand while bottom tower was going down. You killed Yi twice, but your other two lanes were getting wrecked with seemingly no support (well, I say wrecked, Zed was going bot and helping them out, and actually going about even against Riven). Caitlyn got a double kill, Yi took a tower, minions took a tower (I assume mid) while Skarner killed your mid laner.
Overall, it seems like you were mostly focused on your jungle with a bit of support in the top lane throughout the laning phase (just from what I can see from stats; obviously I have no idea what happened in the game and I can only see data)). By the time you guys were able to bring your late game strengths to bear, you were down 5 towers to and even on dragons, but they just had way too much map control from their early game dominance.
