A late try from replacement hooker Sama Malolo gave Samoa some hope late in the contest, but they lacked the accuracy in the difficult conditions and came away without a point.
Argentina wing Emiliano Boffelli scored 16 points that proved the difference in a tight clash in which both defences put in some huge hits and were difficult to break down.
"We made too many mistakes and didn't adapt to the conditions, particularly at the start of the game," Samoa head coach Seilala Mapusua said. "I thought Argentina executed their gameplan really well and we weren't able to adapt.
"We knew that with Boffelli in their team that they could slot them (penalties) from anywhere and getting that yellow card (for fullback Duncan Paia'aua) early on didn't help us.
"We weren't able to get our game going but I'm really proud of the boys' efforts."
Samoa captain Chris Vui was also magnanimous after a defeat which leaves his side in second in Pool D with five points from two games, with fixtures against leaders England and Japan to come.
"I thought the better team won, all credit to Argentina, they were more clinical," Vui said.
"The momentum was swinging our way (after their try) and we thought we could have come back. We've got some learnings to take and a six-day turnaround to take into Japan."