Upvote:2
No.
There is no right (for you as a passenger) to have carry-on luggage; and as safety of the aircraft is paramount, having no place to stow luggage in the cabin is a risk - as it can turn any item into a projectile if there were turbulence.
So the airline is well within their right to stow the luggage in the cargo hold.
Further, many times if this is the case - the luggage is provided to you at the jet-bridge/staircase on arrival.
If you have some medication or other such items in your carry on and you are asked to stow it in the cargo hold; you should remove these items (for obvious reason).
Now, if the airline has a specific fee for carry-on luggage (that is you have to pay for this privilege) then you might be liable for some compensation.
Although, I don't know of any airline that does, but you can never assume things - especially with LCC (low cost carriers).