How does one then show their displeasure with the performance of their fellow player?

The word "bad" is as harmless and tame as it gets, without breaking into flowery prose

or typing out a "How to Play LoL: Beginners" guide in the middle of the game.

me

"stay behind the tank plz"

them

"don't tell me how to play!"

them `dies`

me "plz just sit back a bit"

them "you talk too much **** you"

them `dies`

me "bads being bads"

them "ima report you! `dies`"

"Dear Annie, it positively displeases me when you are playing lik-" an ally has been slain
"MY GOD YOU SUCK"

Honestly, does it not suck the air out of what you're trying to say when you're trying to be "helpful" when they die right in the middle of you typing? I give up there.

There are two things you are not considering here:

1) While you personally may be good and have context on who is bad and good, in my experience, most of the people accusing people of being terrible or whatever are generally not very good themselves. It's just being a jerk with a high opinion of oneself, not an actual difference in skill. In the cases where they are right, it's usually them smurfing or premaking with smurfs, and we don't have a ton of sympathy there either. Matchmaking is pretty effective. There wont generally be 'bads' in your games, just people who are a little better or a little worse on par than you.

2) We want LoL to be a friendly environment in pub games. You can give people feedback without being a ragey jerk. The OP mentioned calling people 'bads'. I am guessing that usually when someone is calling someone a 'bad', they are saying a lot more than that -- which would get you in the tribunal. For example, "You are %#@%$# terrible, you are so bad." or, "Why do I always get stuck with bad players? You guys are totally screwing up my rating. Learn to play."

Honestly, we don't want either of those situations in the game.