The US lost in that it failed in its objective: To preserve an anticommunist government in South Vietnam. Losing a war doesn't mean you end up surrendering. Losing a war means that you didn't achieve your war aims and your enemy achieved theirs.

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Did the US lose a lot on the battlefield? No, not really. As you can see, they typically inflicted very disproportionate casualties against the Communists.

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But, they still lost the war. Regardless of how many enemy soldiers the US can kill, they still had more. They still had people infiltrating South Vietnamese villages and cities and recruiting more. They still had more of them flowing down from the North.

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While it is an immensely complicated topic, a short takeaway is this:

- The US supported South Vietnamese governments were typically inefficient, corrupt, and didn't maintain the loyalty of their people, let alone their own military. Coups, desertions, etc were not uncommon.

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- While the US and allies were able to kill huge numbers of enemies, they were not able to accept a fraction of those losses. Americans lost their enthusiasm to lose thousands of men in a country they never really thought about much to begin with. When the US pulled its troops out, the South Vietnamese government was unable to hold back the Communist advance.

- While the US was squeamish about losses, the Communists were not. They fought for decades, against the French, the Japanese, the French again, the US, and of course a succession of anti-communist governments. They suffered millions of casualties but were capable of motivating their people. It is far different for a Vietnamese to die fighting in his homeland against a foreigner than for an American to die in a country his parents probably couldn't find on a map.

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If you only take casualties into effect, then you can consider Germany to have won both WW1 and WW2. In each of these wars they were able to inflict disproportionate losses against their enemies in comparison to their own. It didn't bring them victory.