Wikipedia:I'm sorry you screwed up
|This essay contains the advice or opinions of one or more Wikipedia contributors. Essays are not Wikipedia policies or guidelines. Some essays represent widespread norms; others only represent minority viewpoints.|
|This page in a nutshell: Some apologies put all the blame somewhere else. Try to say "I'm sorry I screwed up".|
Is it an apology to say "I'm sorry you screwed up"? Clearly not. And yet some Wikipedians feel uncomfortably obliged to accept such statements as apologies, just because they contain the words "I'm sorry" or "I apologize". You are not obliged to accept a self-serving "apology": "I'm sorry if people have misunderstood what I said." (What I said was fine, but some people are just stupid.) And you're definitely not obliged to accept an insinuation that you are the one to blame: "I didn't mean blabla, but I apologize if you took it the wrong way." (Aren't you being a little paranoid? It's not all about you, you know.)
A proper apology avoids the word "if", which suggests the speaker is in flight from accepting any blame that might be going. It also avoids the passive voice, known in this context as the past exonerative: "In hindsight, it is unfortunate that vandalism warning templates were placed on your talk page for edits that were not clearly vandalism." (I still consider your edits vandalism, but I'm getting a lot of blowback on WP:ANI.)
Apologize in the arena where you offended. To apologize in private, for instance by e-mail, for offending in public is a craven way of saving face. 
If you're not sorry for something you did, don't apologize for it. Spare both yourself and the recipient the demeaning "if"-apology, the passive-aggressive apology for someone else's (supposed) feelings, and the private apology for the public offense. You'll both feel better.