Answering for the US, graduate admissions are highly individualized - there's no formula, and decisions are being made by human beings tasked with evaluating a stack of applications that cannot be judged objectively.
All it takes to be admitted to grad school is for at least one admissions committee at a school you apply to to decide you would make a good graduate candidate. All it takes to not be admitted is for all of the admissions committees to feel they have better alternative candidates. How exactly that shakes out depends on some mix of the content of your application, the criteria each committee member considers, and the content of every other application they review.
If a program you apply to conducts interviews, you can expect to get questions about an outlier grade like this one. If you get to that stage, whether or not you are ultimately accepted may hinge on how exactly you answer that question. Some people have good excuses for specific poor grades, such as medical or other life events, in which case honestly explaining the situation is straightforward though balancing personal privacy is another important factor.
Your reason is that you got caught cheating. You may be tempted lie or deflect about it, by not mentioning it or using wording like you originally did with this question: saying you had a falling out with a professor, or that you electively took a failing grade in order to take a different course. I think you can expect admissions committee members to see through this sort of thing, and even if they don't it doesn't exactly paint you in the best light.
Being more straightforward about what happened may be a better route, but it's important that you're sincerely contrite. Students caught cheating (or really anyone "caught" for anything) have a tendency to deflect and minimize. In your own question, you write both "I didn't properly cite some work" and "the fault is all mine" - this does not resonate as honesty with me. While you write words accepting blame, "not citing properly" is not typically the level of plagiarism that nukes your grade. "Not citing properly" sounds more like citing the wrong source, or when you break up statements during editing such that a citation for multiple items A,B,C seems like it only applies to C, or disagreements over the lines between common knowledge and what must be cited. If it's really that sort of issue, you should be contesting this at your current institution, as these are all reasons to lose marks on an assignment but not reasons to be failed in a course. On the other hand, if you have "not cited properly" by presenting work that is not your own (or partially not your own) as if it is your own, you've simply plagiarized which is cheating.
It's also possible there won't be too much attention on this one course and you will be accepted without it coming up because an admissions committee will see it as an unimportant outlier in an otherwise strong application.