They were a converted try away from making the tournament's last four for only the second time, but sustained late pressure failed to yield the decisive score.
Hadden, however, believes his team's form in the World Cup is a good sign for the future, and tipped them to challenge for the RBS 6 Nations Championship title within three years.
"I'm very confident our young side will learn from this," he said.
"Some of these youngsters have matured in a very short space of time.
"I believe that in the next two or three Six Nations, we'll be a serious threat and a side to be reckoned with."
Scotland were lacklustre in an error-strewn opening half last night, and could only manage a penalty apiece from Dan Parks and Chris Paterson as they went into the break 13-6 down.
A try by Longo Elia, dovetailed by a conversion and two penalties by Felipe Contepomi, gave the Pumas a half-time lead and their defence was hardly breached once by the negative Scots.
It was only when Argentina had forged further ahead, thanks to another Contepomi penalty and a drop-goal by Juan Martin Hernandez, that Scotland showed an attacking edge.
They dispensed with their kicking game and chose to run with the ball, and it yielded a try by Chris Cusiter which was converted by Paterson. Their late onslaught failed to yield dividends, though.
Hadden defended Scotland's kicking gameplan even though the late change in tactics almost paid dividends, claiming it was the only way to unlock opposition defences at the World Cup.
"In the quarter-finals there hasn't been a massive amount of rugby played," he said.
"That's because referees are allowing a much bigger contest for the ball at the breakdown and defences are coming up so fast in attack and applying enormous pressure.
"That makes it difficult to play a fluid game. Most of the games have been tight and tense affairs and nobody has been able to establish any rhythm.
"That was the tale of the match. Argentina's territorial advantage was the crucial factor."
Hadden felt his side just ran out of time, adding: "Had the game gone on five or 10 minutes longer, we might have won.
"Argentina played a very good game and had a stranglehold until the final quarter that was difficult to do anything about.
"Argentina were streetwise and sharp which makes it hard to get going, and they put pressure on us at the breakdown and set-piece.
"Thankfully they tired and we managed to get some rhythm. We had an opportunity at the other end, but we just weren't clinical enough to do what we wanted to for our long-suffering fans, which was to take them to a World Cup semi-final."