The Huns actually did attack the ERE. The details are sketchy because some of the primary sources are missing but the Huns appeared victorious. However we do have records in which ERE sent an embassy to the Huns negotiating a yearly tribute in exchange for peace. The payment was later doubled which the ERE had to agree too.

The Huns ravaged much of the Balkans (which were already not in the best of shape after previous wars) however they were not in a position to lay siege on Constantinople and its impenetrable walls. So the switched focus to attack the west instead.