Emirates doesn't owe you anything in connection with your missed separately ticketed flight. I would always plan to spend the night when separately booking an onward flight coming in off of a long international flight....too high of a risk for a misconnect. This is where trip insurance would have been useful, especially having set up a too-short connecting time on your own. Unfortunately I can't offer any advice other than to chalk it up to experience and a lesson learned for next time.