Carry-On Not Included?

Are you referring to any particular airline?

You need to id the airline since every airline has it own policy regarding carry on. And the type of ticket you are buying. Some of the sub economy tickets, United for example, does not permit a carry on bag beyond a personal item in the super economy ticket class.

Sure. I believe it was Lufthansa operated by Air Italia I think?

Didn't know that about United.

Not included means you don’t get a carry on. What you are describing sounds like United’s ”Basic Economy” rather than their standard ”Economy”.

You need to check the class descriptions for the airline. For example, United has ”Economy” which gets you a seat selection, checked bag, change with a fee, etc. United also has ”Basic Economy” which is cheaper and you don’t get any of those things. There are even more variations and different airlines use different terminology.

United Economy
https://www.united.com/ual/en/us/fly/travel/inflight/cabin/economy.html

United Basic Economy
https://www.united.com/ual/en/us/fly/travel/inflight/basic-economy.html

Here's what Lufthansa's website says will be free, depending on class of ticket. You can click through to other information if I've misunderstood your question.

Thanks all! I'll have to check the class of fare again.

Usually basic economy doesn’t include a carry on, but you can purchase it for extra. However, for transatlantic flights, I have not come across an airline that doesn’t include the carry on even for basic economy (as basic economy is all I fly). If it is a flight within Europe, the carry on bag is probably an extra fee.

Some airline sites have separate links to cabin baggage and checked baggage. Be sure to look at both.

I believe it was Lufthansa operated by Air Italia I think?

Alitalia is not a member of the StarAlliance network that Lufthansa belongs to,
and Air Italy has ceased operations in 2020. LH is allowing
one carry-on up to 8 kg in "Econonmy Light".

Here is a link to Aer Lingus in which the airline describes its carryon policy. You can pay to bring a carryon on flights within Europe.....

https://www.aerlingus.com/travel-information/baggage-information/cabin-baggage/

This does sound like the United Basic Economy fare, which is essentially click bait for the unwary since it doesn't include much of anything. Once booked you'll then be nickle and dimed for a variety of "upgrades" ... all of which you probably assumed would be included in the original price, including things like seat selection, baggage fees (including carry-ons, etc.) .
It's one of those cases when you're probably better off just springing for the upgraded fare from the get-go (in this case full-price economy) if it includes most of the things you'd otherwise be paying ala carte for - will probably be cheaper in the long run.

Thanks again all. I didn't actually click on a particular fare, just a particular flight, so I'm not sure why that fare showed up for me. Glad I am forwarded.

Most people are seeking the cheapest fare so that is what usually shows up when you do a flight search without choosing your class of service.

Remember, even when paying for a carry on you have to stay within the size AND weight limits.