Okay. Sorry if I was a bit rude earlier, but I've run into a lot of people raging on smurf accounts lately and unfairly assumed you were one of them. My bad.
I think the main issue that game was one of team composition. Your team seemed like it would focus on mid game picks from Lee Sin, Kha'zix, and Twisted Fate to allow you to pressure objectives. In comparison, the enemy team had good teamfighting (Nautilus, Lissandra, Thresh) and diving. Considering how durable the enemy team was, you would have difficulty killing their frontline (Thresh, Irelia, Nautilus). Your team had Janna to disengage and protect Caitlyn, but Lee Sin and Kha'zix would want to dive the enemy backline, so your focus is split.
Irelia's only really job in that game was to dive your teams backline (Caitlyn, TF, Janna) and distract them while their team killed Lee Sin and Kha'zix. Your backline didn't really have any defense against her damage, so her base damage and Sheen procs were sufficient to kill them due to their low armor and health.