My understanding is that the 'flu shot' changes every year, in anticipation of the strains predicted to be the most prevalent that year.
In other words, flu shot producers say "we think flu strains A, B, and C will spread this year" and strains B, C, and D may be what actually spread.
It's still worth getting because even if you catch strain D, your immune system still easily defeated B and C when exposed and you didn't even notice.
Without some serious testing you're not likely to know what you got.
But even if we assume you did catch the flu, there have been long term effects that show that regular flu shots over a few years lessens the severity, occurrences of serious problems with the flu. So the benefits seem to go beyond a given vaccine.
With flu vaccines there seems to be both a specific benefit, but also more general benefit longer term.
In fact, if you read the experts, you'll see the the flu shot is generally a cocktail against the most prevalent strains. Since strains are left out, it's absolutely known that the flu shot will not protect you against all influenza strains.
See this page for information on how strains are selected: https://www.cdc.gov/flu/prevent/vaccine-selection.htm
The flu shot is not a magical guarantee that you personally won't get the flu. What it does do is lower the rate of transmission for the flu significantly, by improving the herd immunity.
People need to understand that getting the flu shot is less about helping yourself, and more about helping your community. Think of it like giving blood. It's an altruistic action that you can take to help others around you.
Vaccinations are very effective protective measures. Just not at protecting against stuff that isn't in their narrow scope.
² I believe the actual numbers are something like 80 % for the flu: people vaccinated against flu strain X only contract it at 20 % the rate of unvaccinated people, or numbers to that effect