The Allies knew the logistics were an issue; so did the Germans. The German strategy was to deprive the Allies of a serviceable port. Brest and Cherbourg were captured after hard fighting, and the Germans thoroughly destroyed the port facilities. Most other ports were garrisoned and held out through May 1945. The Allied temporary solution was the Mulberry, although only one survived the June storm.
Of course, once we had supplies coming through Antwerp, Hitler made that the objective in the Bulge offensive.