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An example of what I'm referring to would be a scene in Deadpool 2, where, to be "meta," Deadpool says "that's just lazy writing." I didn't find it funny, because the plot point he was referring to was genuinely lazily written. The writer thought acknowledging their laziness without making effort to be genuinely clever, was clever. It's a very smug way people attempt to avoid criticism, I suppose. Everyone does it, consciously or not, out of insecurity or for humorous intent. The mentality of "I know the issue exists, but because I don't want to/know how to fix it, I'll just pretend acknowledging it is good enough."

Example sentence: "The insecure writer desperately attempted to avoid criticism for the flaws he was aware of by _______, rather than putting effort into fixing them."

Lampshading?

Lampshading is the writers' trick of dealing with any element of the story that threatens the audience's Willing Suspension of Disbelief, whether a very implausible plot development, or a particularly blatant use of a trope, by calling attention to it and simply moving on.

I don't know if there's really a formal literally technique with a formal name but it looked to me like a "pre-emptive confession."

Some searching around brought up a relevant mention of the phrase by social anthropologist Kate Fox in "Watching the English: The Hidden Rules of English Behaviour":

A less charitable interpretation would see anthropologists' ritual self-abasements as a disingenuous attempt to deflect criticism by pre-emptive confession of their failings – like the selfish and neglectful lover who says 'Oh I'm so selfish and neglectful, I don't know why you put up with me,' relying on our belief that such awareness and candid acknowledgment of a fault is almost as virtuous as not having it. (emphasis mine)

Note the description "relying on our belief that such awareness and candid acknowledgment of a fault is almost as virtuous as not having it."

See also:

Waldron et al., "Communicating Forgiveness," p.98

Paul Mann, "Masocriticism" p.51

"Aesopic-Proverbs-11-20" sententiaeantiquae (blog)

Ron Charles, "Sex and the middle-aged man," Washington Post, July 3, 2017:

Yes, he’s spoiled and selfish and shockingly immature, but he’s also disarmingly contrite, and it’s hard to accuse him of any lapse that he hasn’t already crucified himself for. He’s mastered that male art of moral self-defense through preemptive confession. (emphasis mine)