Winchester was an outdoor cat when I got him, and after we moved into a new place where I didn't know any of the neighbors, I refused to let him out for fear of what might happen to him.
He just about drove us nuts with his whining!
He calmed down quite a bit after we got him neutered, but would still occasionally "beg" to go out, or try to sneak out when we opened the door. He could care less about going out, now.
A couple of years ago, I was living in a very small travel-trailer (looong story) and poor Maverick & Gabriel were confined in that small place: I felt so badly for them.
The landlord built a fence around the place, so I could at least let them out into the yard to run around a little. What a mistake that
They got a taste of the great outdoors, and after we moved, I wouldn't let them out anymore, either. They weren't very happy about it - anymore than Winchester was. But they eventually got over it (although they wouldn't hesitate to have their fun if I let them out again!) and eventually quit pestering us once they realized they weren't going to get their way...
Spencer, for some reason, never cared about going out again once my s/o brought him home. I think it's b/c of the abuse he suffered before we got him, and he's so grateful to have a good home that he's purr-fectly content to be an indoor kitty. I think he remembers the horrors he had to endure while he was an outdoor cat, and has no desire to go through that
Give your furbaby time: he'll adjust, and give up when he realizes his whining isn't going to do him any good..