User christian.p had some excellent suggestions which I will recap:
Don't make him feel stupid: This will illicit irrational emotional based responses.
Look for other tools that perform Task Y: This shows that you genuinely wish to help him solve the problem by offerring alternatives.
Provide quote for custom development of Y feature: This shows you aren't lazy and gives him the impression that you aren't brushing him off.
What I would like to add is that you should try to see this through the management perspective. I am sure it doesn't surprise you that there are a LOT of worthless software developers and IT professionals in the field, and your manager has probably been around the block enough times that he had the misfortune of managing a number of such individuals.
Managers get told "Y is impossible" by supposed "professionals" all the time that are either tragically misinformed, blatantly untrue, or scandalously deceitful. Many of them figure this out later talking to a more qualified technical person or figure these things out years later after said person had already left the company and the new guy rolls in and actually does the imaginative impossible.
Where I work now my manager had a number of myths about the capabilities of the technology platform we are working under, fed by the previous development team (and if the abysmal quality of their code speaks to their skill level then it is not flattering). I prototyped and implemented a number of game changing things on top of meeting deadlines and goals and now my manager trusts me.
Earning your managers trust is the only way to actually avoid the annoying leg work of proving your assertions. Now that I have his trust I can tell him that something is "an extreme challenge" (I NEVER use the word impossible to describe anything), and he takes my word for it.