Lautaro Martinez scored a hat-trick before being substituted at half-time, with all four goals coming in the first 45 minutes.
Martino explained: "I do not think this is our reality - nor do I believe that having 11 games without losing is our reality.
"Of the 'A' class [of team], this is the second game we played - the first was against Chile and the substantial difference is that tonight we made mistakes.
"Argentina could hurt us because there were 15 minutes where we played well and then the breakdown starts from an error.
"To learn from this, we need to play more major games of this stature. We must look to try to compete with the best in order to be able to take that leap we want to take."
LA Galaxy midfielder Jonathan dos Santos offered a similar assessment, frustrated by Argentina's ability to punish Mexico, who dominated possession but were outdone on the break.
"I think the team started well," he said. "I feel that the goals for Argentina were more our mistakes than their successes. We know that we cannot make these mistakes against these teams.
"We have to lift our heads, we are still working very well. The team is confident and I think it is a defeat that will make us learn."