The US lost prestige in the war. It did not surrender the war. The US has difficulty figuring irregular wars. Once we started prematurely leaving it turned from regular (where the US won) to irregular. We haven't found a way to successfully disengage from an enemy intent on waiting it out. We still have difficulty because the amount of boots in the ground needed is high for our doctrine (superior firepower).
Still it wasn't a loss in a military sense. Win every battle lose the war kind of thing because it was a political loss. It was not a surrender though. The nips surrendered in the Missouri in Tokyo bay when they lost everything. Then we remade them in our image. They play baseball in Japan. Do we play hide Charlie or whatever the f**k the Vietnamese play? No. We didn't surrender. We cut or losses and left. I'll say the us lost but we never surrendered.