Former Barcelona boss Martino was appointed El Tri coach in January and enjoyed a sensational start to his new role, beating Chile in a March friendly and then winning the CONCACAF Gold Cup.
But an 11-match unbeaten run came to an end on Tuesday as Argentina, Martino's former team and the last side to have beaten Mexico before their streak, ran out 4-0 winners in San Antonio.
Lautaro Martinez scored a hat-trick before being substituted at half-time, with all four goals coming in the first 45 minutes.
"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.
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.
- Mexico's top team given lesson as it fails Argentina testGoal.com
- Argentina drub Mexico on Martinez's hat trickESPN
- Argentina silences Mexico and its followingHouston Chronicle
- Martino: Argentina hammering isn't Mexico's reality - but neither is 11 games unbeatenGoal.com
- Martinez delighted after first Argentina hat-trickGoal.com
- Watch: Lautaro Martinez Hat Trick Sparks Argentina Rout of MexicoSports Illustrated
- Lautaro Martinez 'happy and excited' after first international hat-trickThe Statesman
- Martinez hat-trick fires Argentina over MexicoSport24 (blog)
- Lautaro Martinez's hat-trick sees Argentina smash MexicoSBS - The World Game