We had that war won in 1970; the North was seriously considering pursuing some sort of truce, which would have probably left South Vietnam a free and prosperous country like South Korea.
Then, Jane Fonda and John Kerry convinced them to "hang in there" while they worked on convincing the traitors in Congress to give up.
You are correct that our military did not lose the war in Vietnam. However, when the political aims of the war are not met, that war is “lost”. We left that conflict in a most shameful manner, and allowed our friends to be overwhelmed and butchered. Yeah, we lost that war.