But late tries from Lee Byrne and Shane Williams, together with Gareth Delve's earlier score, gave the visitors some cheer.
And despite the hard lessons, Jenkins insisted he and his team will take something from the trip.
"I've learned lots of things from this tour," said the former British & Irish Lions coach. "A lot will come out of this tour, we will go forward from here.
"You have to compete physically. We did last week and we didn't in the second Test and so the best team won on the day.
"Our lineout didn't work at all when it was outstanding the previous week and our set-piece was pressurised so we never got the game we needed to go forward.
"They had a lot more pressure physically and possession-wiseÂ and we had to defend against a very aggressive team.
"They were clinical and very impressive but we had a little bit of possession in the end and scored those few tries, but we were denied the ball for long periods.
"If one thing tires you out it's not having the ball and having to defend."
Wales captain Duncan Jones insisted the tourists could not hide behind the lack of experience in the Dragons' side after the disappointing display.
"There can be no excuses because Argentina deserved their win," insisted Jones, captaining Wales for a second time on the South American tour.
"They made it very, very difficult for us but we caused a lot of problems for ourselves - that's not detracting from Argentina because they took their chances so they deserved their victory.
"Still, I think all the boys who played out here have taken huge steps forward and they take a lot of pride from it because they've put their hands up for international jerseys and they will keep working.
"We're still a disappointed squad but at the same time we come away from this tour with a lot more experience.
"But still we can't use the fact we have a young squad as an excuse because we came out here to win the Test series and we haven't done that.
"But we've come away and learned a lot and that can only hold us in good stead when it comes to the autumn internationals and the Six Nations."