Gernot Rohr's side fought back from a two-goal deficit to hand a 4-2 defeat to La Albiceleste in November's friendly encounter at Krasnodar.
And the Paris-Saint Germain winger spoke about how their task was made 'difficult' with the talismanic forward absent for the tie.
“I love playing with him [Messi], the best thing that can happen to a player is to play with the best and with the aliens, you value playing with him…,” Di Maria told Fox Sports Radio.
“Everybody has a good time in the clubs and in the national team when Leo is not there all of us want to assume that role, but being so used to playing with him it is difficult when he is not in.
“We all try to do our best, good first half against Nigeria and then the game got away, it got out of hand but at times we do things right.”
Di Maria and Messi, however, have a chance to avenge just their second loss to the West African side when both sides clash in the final Russia 2018 World Cup Group D match in Saint Petersburg on June 26.