I can understand that you don't want to put any money into something that this cheapskate landlord will own when you leave! You haven't said how large the room is, but you can purchase carpet as wide as 15 feet (common width is 12 feet), in how ever many running feet you need. You can then put it down using carpet tape. Carpet tape is a heavy duty double-stick tape. When you move, just roll up the carpet, pull up the tape, and off you go (with the carpet). Leave him with his yucky brown, broken tile.
Did you get it in writing that he permitted you to pull up the old carpet?