Americans have been sold an image of the US being an omnipotent presence, due to its Navy. It is a legitimate question to wonder why a relatively weak, long embargoed country has the power to control the waters when the US has spent a pretty penny on all these warplanes and aircraft carriers.
If little Iran can prevent the US from being able to establish security in a little straight, it (ideally) shatters that image and causes some soul searching for what US taxpayers are buying with the military.
The situation is massively favourable to Iran, from a strategic point of view. The Gulf is narrow, bordered by Iran all the way and with mountains and rugged terrain nearby, which is very convenient to hide rockets. What a carrier brings is completely irrelevant in this configuration.
Iran does not 'control the waters', it is denying access; this is an importance difference. Lacking control means that Iran cannot make use of many of its naval assets, which they have invested in.
You over estimate the American publics capacity for critical thought and reflection. Most Americans will come away from this humiliation thinking we just need to increase the military budget
You can lose a game of chess to a guy with fewer and less powerful pieces than you if you play like a moron. The US has been playing the Iran situation like a gigantic moron.