Was there an admission that America had 'lost' the war and is it right to describe it as a war lost?
It's clearly an area of history I know little of.
No it isn't right to call it a lost war. The US transferred the burden of defense to the American trained south Vietnam army. Signed an armistice and pulled out in '72. But once us troops were out north Vietnam continued the war and crushed the south in '75.
The war the US lost was the fight for public opinion. The US never lost a major battle, even the famous tet offensive was a massive militarily defeat for the north but the public got tired of hearing about the war