My cat pooped in room that we have recently closed off.Is this a form of middening?

We decided to no longer allow our cats access to our bedroom so we close the door now all the time.
They have had access to the room and slept their a lot during the day, but we felt it was unhygienic and they have a huge house at their disposal. So everything was fine, they occasionally got in once or twice over the weekend which was fine I didn't want to be too strict. But low and behold we had a territorial poo on the carpet right beside the bed. I want to continue to close this room off but I also don't want any more surprises how can I gradually train them to stop because they won't be allowed in the room?

They are more likely to "stake their claim" to a room they rarely get access to than they are to rooms they are freely allowed in.  I don't think you can be halfway with this room.  It either needs to be off limits or totally open as it was before.  In my experience, they will mark their claim to the room either by spraying or using its litter box (if it has one) every time they get into it.