The Portugal international was unhappy with the performances of a number of his team-mates and focused much of his displeasure on the Argentine winger
Jose Mourinho's men went down 2-1 and only a late strike from Cristiano Ronaldo salvaged his side some hope ahead of the second-leg.
Following the defeat, the Portuguese tactician was highly critical of his players, suggesting their performance had left much to be desired.
Television cameras have shown that Mourinho was not alone in his discontent with some of his squad, with Pepe seen remonstrating with Di Maria in the opening 45 minutes.
The 29-year-old appeared to convey his displeasure to the Argentine a number of times, gesticulating that he needed "to play with more desire" and "show his face".
Di Maria was withdrawn from the action at half-time by Mourinho, who hinted he would be taking further action against one of his men.
"One player did not want to play and I will have words with him," he told reporters.
The Argentina international has four goals to his name in 24 appearances in all competitions this season.