Rory Lamont ran in an 11th-minute try and Gordon Ross kicked eight points to give the Scots an unconvincing 13-9 victory over a spirited USA side.
Head coach Hadden said: "I never thought we'd concede the game as the Americans didn't really threaten.
"They could have had the ball in our 22 all day and I still don't think they would have scored without kicking a few goals.
"I was never concerned but I'm disappointed we did not take a few more of the opportunities we had. We got good field positions but they defended well."
Scotland's starting line-up contained 10 capped internationals but few of them will have enhanced their chances of making it to the World Cup.
Hadden maintained the laborious display came as little surprise given it was a scratch team that met for the first time on Sunday.
He said: "The history of A team rugby is it's fairly scrappy stuff. We don't have a history of looking smooth and well organised at this level.
"It's a reminder of how long it takes to create a platform to win a match and we never created that first phase platform.
"(Forwards coach) George Graham was tearing his hair out at the set pieces and they will be the key areas we work on.
"Once we won ball we looked quite threatening but we didn't win enough of the set piece ball that we needed to put them away."
USA skipper Francois Viljoen kicked all of his side's points and head coach Peter Thorburn was delighted with the improvement following Friday's drubbing by England Saxons.
The Kiwi said: "It was a big improvement on last week. I don't care what anyone says, we weren't nearly as bad as 51-3.
"We've worked hard since then and I was very proud with the way our forwards in particular came through. Our kicking out of hand wasn't very accurate.
"Our scrum was outstanding, on their ball as well as ours. Our driving was great as well and the forwards were great.
"We have a big pack and they'll be a hard set of forwards once they learn to play the game.
"But Scotland deserved to win as we played too much of the game in our half."