Upvote:35
As a general practice, making sure you are admissible in destination country is your responsibility. Airlines usually verify closely, as they have to transport you back to your origin (or your home country) and may have to pay a fine, as they allowed passenger without proper documents. They obviously made a mistake here. But, its ultimately your responsibility and airline does not owe you anything.
For travel insurance, it can vary. But not securing proper documents is still your problem and a situation that's totally within your control. Some insurance may accept a claim, but mostly your are out of luck on this.
Chalk it up as a learning opportunity and make sure you double check the visa requirements and documents needed for admission, even before booking the ticket.