Haha! I wondered if it could not mean: the shoes do not pinch my feet, so I do not feel the shoes as opposed to I do not feel my feet any longer...
Some of the sentences used seem to be responses to specific situations. I do not believe that because a sentence is not common or used in everyday circumstances that it should not be learned.
I imagined someone looking for their shoes underneath a blanket or something but this is a good idea as well.
"Feel" is used this way by many in the US. But I imagine that many people would find it odd.
Example - One might be told that a pair of shoes are under the bed. While feeling for (or looking for) pair a shoe under the bed, one might reply back "I do not feel the shoes." - best guess
On American Idol, judge Randy Jackson is famous for saying he doesn't 'feel' a performance - meaning, he doesn't like it. "I'm not feeling it, man."