They proved you wrong, at great cost.
A more correct and polite version of your advice: "It will cost us a lot more to ship this as-is, and fix it later, than it will to delay shipment and fix it now. Is it too late to do that? Did we over-commit to shipping now?"
It wasn't your responsibility to come up with that version. It was your manager's responsibility. It was also their responsibility to find the necessary decision-makers and involve them directly. I would argue that this sort of work is the only real way that "management" can provide value in the first place.
Somehow, socially, it's incredibly common for people to value the inverse of that job. People assume it is "good work" for a manager to successfully ignore unpopular concerns, and push through to the end, no matter how inefficient that makes the journey.
That works out in the case that the shipping date was over committed, such that a delay would cost more than fixing it later. Even so, that entire situation would be avoided by refusing to over-commit shipping dates in the first place. That's the same responsibility applied earlier in time, so a manager that behaves the way I have described could factor out the entire problem at its source.
This is what the average person should learn about management. Even if it's not their job personally, there is a lot of leverage behind the decision a worker makes about what management behaviors to socially favor, and what behaviors to socially reject. That leverage is multiplied at every level up the hierarchy, making that the opinion of someone in a management role is very significant, and the opinion of someone in an executive role is crucial.
It's really difficult to be explicit about opinions. You can't really put them in your resume, but at the same time, an opinion on management style may be an executive's primary value contribution!