Leicester scrum-half Youngs, a second-half replacement for Richard Wigglesworth, scored the only try of the match 12 minutes from time with England trailing 9-3 against the Pumas.
Jonny Wilkinson, who missed five penalties, kicked the conversion and unconvincing England held on for a hard-earned 13-9 victory.
Tindall paid tribute to the impact made by Youngs who was making his first appearance since undergoing knee surgery in the summer.
"Youngsy came on and turned the game for us," Tindall told ITV. "We got our tempo going and we got a try on the back of it.
"The one thing I am going to give the team credit for is the way we stuck to our task. We got a win but there is a lot to work on."
Argentina dominated the first half and England had no answer.
"We were under no illusions about what Argentina can bring," said Tindall. "For the first 20 minutes it is hard to play rugby when you don't touch the ball or see it.
"We know how good their pack is and they kept the ball really well. They squeezed and squeezed and they won their penalties.
"We gave away three easy penalties away and from then on it makes it hard work for you."
Tindall acknowledged that England will have to work hard on improving their discipline ahead of their remaining Pool B matches.
"You've got to play to what you are getting away with and we were not squeaky clean enough. It is something to go away and look at."
England manager Martin Johnson was far from pleased with the performance, but was happy to have got the win.
"I aged about 20 years today," he said. "But we said before that's what World Cups are about. You will get penalties against you, the bounce of the ball won't go your way and you have to find a way to win.
"We got the win. It wasn't a fantastic performance by any means, but a fantastic win in the circumstances.
"We got quicker ball in the second half, we wanted space out wide and when we went wide we got turned over a lot.
"We had to keep going. We always thought if we kept going we'd get there."
Match-winner Youngs felt that getting quick ball was the key to the victory.
"The coaches see these things, and me and (Toby) Flood saw it on the bench that if we played at a high tempo we'd put them on the back foot," he said.
"We looked at our best when we did that and it just happened that I could finish up a try.
"The team we have is fantastic with lots of leaders all over the pitch. It's about getting the tempo right and, if we don't do that, we struggle."
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