One would think the effect of the invention and mass production of the breech-loading rifle, the Gatling Gun, long range artillery and canister, and ironclad ships would have had more effect than it did. Mainly it led to higher casualties, but no obvious or major change in unit tactics.
It is often said that "technology was ahead of the tactics" in the Civil War, which is undoubtedly true. The entire US economy and industry in both sectors of the country was organized around the war effort, the first time America had fully done so. This meant the advances in technology for the time were rapid and devastating on the battlefield.
With the advent of the first machine gun in 1862, traditional units in line tactics became even more suicidal than they had been before. You would think this would have led to more emphasis on mobility and cavalry use, or to flanking movements by smaller units, but for the most part it did not.
When the USS Monitor and USS Virginia fought it out inconclusively in the first iron navy battle, it made every other wooden ship on Earth obsolete. A successful effort to build more may have led to a significant breach of the Union blockade, but no concerted effort was made. The first use of the breach-loading repeating rifle took place during Sherman's March in 1864, and the South had no effective counter in terms of technology and tactics.
So the answer to your question is, surprisingly, very little effect at all.