I personally think you'd be better off not taking feast, butcher or fleet of foot masteries instead getting unyielding, veteran scar's and juggernaut. Yi's ult already gives him enough movement speed tbh, feast is under powered imo and butcher shouldn't be needed unless you aren't good at last hitting minions in which case you should practice last hitting minions. Especially with an attack speed focused champ it should be easy to last hit.
Irelia got a thornmail which just makes it so much harder for attack speed champions as Yi. Idk how you played that game but i woulda just hugged tower and farmed till i got ganks or till lane phase over and would have tried to get fed else where. Youumos and Last Whisper means you will deal more damage to her fast but also you will take that 30% damage, fast. Again, idk how you played but Yi has some cool tricks, his Q can help you escape, and evade an enemy spell/turret shot, also his W can help you not just heal but take a lot less damage from both enemy turrets and from an enemy attack.
Bloodthirster would have been a better choice than last whisperer if she already had that thornmail or you knew thats what she was most likely going for because it woulda gave you good AD which works well with Yi and the LS woulda helped you not lose so much hp from her thornmail. Again Bloodthirster over IE if she had or was getting thornmail because IE woulda just helped you die faster.
Irelia is a bully champ and that was a tough match up for you, no worries. Learn, move on.