Billy Stark's new-look side lost both goals from long throw-ins to the Los Angeles Galaxy player in the match in Marbella on Friday afternoon and were unable to recover.
To add to a miserable day, Ryan Jack, who captained the side for the first time, was carried off on a stretcher after twisting his right ankle and although the extent of the injury is still unclear, the Aberdeen defender will play no part in the friendly against Canada on Monday afternoon.
Despite temperatures at the Marbella Football Center reaching 25 degrees at kick-off, the heat seemed to have little affect on the young Scots in the early stages
Aberdeen defender Clark Robertson found space inside the USA half on four minutes and unleashed a venomous shot which flew just past the post.
In the 18th minute Celtic striker Tony Watt made space for himself on the edge of the USA box and forced goalkeeper Kendal McIntosh into a flying save.
However, two minutes later the Scots went behind when goalkeeper Jordan Archer dropped a long throw-in which left Villarreal with the simple task of tapping the ball into the empty net.
USA almost doubled their lead minutes later when the ball fell for Mario Rodriguez but the striker sliced his shot past the post.
Scotland tried to find their way back into the match and Stuart Armstrong forced McIntosh into another great save when he aimed a shot towards the top corner of the net.
But on the half-hour USA were 2-0 in front when Stark's side failed to learn their lesson from the first goal. Another long throw-in went deep into the Scotland box and the unmarked Villarreal headed the ball across the goal and beyond Archer.
Stark made a number of substitutions after the break with Kieran Duffie replacing the injured Jack on 55 minutes but to no avail.
Scotland stepped up their efforts with Livingston midfielder Stefan Scougall a constant threat going forward but they were unable to create any real chances.