The World Cup runners-up went down to Raphael Guerreiro's stoppage-time header in a friendly at Old Trafford, despite having had the better openings throughout.
Lionel Messi hit the post early on, while Di Maria also went close in what was a low-key affair in Manchester.
Di Maria took a heavy blow to the foot in a challenge with Nani during the first half, but was able to continue until being replaced shortly after the hour mark by Erik Lamela.
Despite the injury, the Manchester United man was hopeful of being able to feature in Saturday's Premier League clash at Arsenal.
"It was just a blow," he said. "I hope it doesn't swell any more so I can play at the weekend."
Coach Gerardo Martino added: "We don't think it's anything serious, it was quite a tough blow he took.
"It was a tough knock. It cut the skin a little bit. But we have had a look at it and we are evaluating the situation.
"We are having a look at some X-rays, some images that have been taken but in spite of that we don't think it is too serious."
On the game itself, Martino felt his side had done enough to secure victory before Guerreiro's late winner.
"We've done all the merits to win, we had the best scoring chances," he said.
"The result changes the mood, but it was a very good match for Argentina. In the different facets of the game in which we want to have supremacy over the rival, we have done so."
The pre-match build up was dominated by talk of a meeting between Messi and Cristiano Ronaldo, but both men were substituted at half-time.
"On the change of Cristiano we had no idea," Martino said. "About Messi what we had agreed upon, we had talked about it because he had played throughout the game against Croatia."
