The Scots were holding a commanding 28-13 lead with 30 minutes left to play Santiago Del Estero after Duhan van der Merwe and Ewan Ashman had crossed for tries. Argentina launched a fightback, however, and sealed a 34-31 victory with a try from Edinburgh wing Emiliano Boffelli, who also slotted the conversion.
Despite the defeat which meant Argentina won the three-Test series 2-1, Gregor Townsend still has words of praise for his players.
"We are obviously really disappointed because we were ahead for most of the game and we had chances - chances to score a try and were held up over the line, and chances just to be a bit more efficient with our exiting in the last five minutes," he told Sky Sports.
"I really feel for the players because so much of their display was full of courage and skill.
"It was our best display of the tour and would have been a famous win but the feelings just now are the opposite of that.
"The way we played away home in front of noisy crowd, against a very good side, I am so proud of that effort.
"We just need to make sure we win those games that we dominate for so long."
With Scotland 31-27 ahead during the final quarter, the visitors opted to kick for the corner instead of taking a shot at goal.
"We got 15 ahead by kicking towards the corner in the first half," said Townsend.
"We backed ourselves and just didn't get the ball over the try line. That was unfortunate but it was something we will learn as a group."