I suspect that the long term impact of the loss of New Orleans falls in two areas: manpower and industrial capacity.
If memory serves, New Orleans and its environs had a population of about 250,000. By April of 1862, a substantial number of its younger male population were already under the colors and elsewhere. Just how many of them were skilled workers needed to keep the city's industrial heart employed is an interesting question. Another question is just how valuable the industrial plant was to the south if northern forces interrupted the raw materials needed for manufacture. It can be argued that North and Central Alabama became the industrial belt of the south during the war, primarily because of continuing access to coal and iron. How much of these materials would have reached New Orleans even if still held with a deteriorating transportation structure is worth consideration. The engine shops and foundrys would probably have been the most valuable assets in the long term due to the blockade. I do know that key technicians (mechanics) were known to pass through the Union lines to places like Mobile and Selma. Also, as the war progressed, a slow process of training new mechanics was underway. This included substitution of slaves and freemen into highly skilled occupations. One source claims that up to 50% of the skilled labor in CSN run industrial plants were black. Southerners showed the capacity to adjust to the new conditions, but in most cases couldn't do it in enough quantity or fast enough to tip the scales toward survival of the Confederacy.