But that wasn't the only time the national boss chose to neglect the Tottenham winger this summer.
Indeed, the 23-year-old barely played all tournament long as he watched Argentina reach the final and lose to Chile on penalties.
And that poor foresight may have created another problem, added to the seemingly unsolvable puzzle of what to do with Emmanuel Adebayor and the fight to hold onto Hugo Lloris, for Spurs this summer. Not a disastrous one, by any means, but one that won't help the north London side.
Not only will Lamela now have to deal with the disappointment of his country losing - that much would be inevitable even had he watched all the way from White Hart Lane - but the winger will have to deal with the fact Martino has no trust in him and didn't let him get the opportunity to show what could have been.
His lack of game time will also do nothing for his confidence, form or fitness, while this could have been time spent training with Tottenham. Yes, several internationals are yet to link up with the north London side's main squad - but the likes of Jan Vertonghen and Christian Eriksen are far more established at the Lane than the 23-year-old currently is.
He could have used every day possible in a bid to enjoy a far more productive campaign next term.
Lamela has also been linked with a move away from Tottenham this summer, by the London Evening Standard among others, and could really have done with this time off to get his head settled - instead of simply having the best seat in the house to watch the majority of Argentina's games.
It may only prove a minor stumbling block - but Martino would have been better off not wasting everyone's time.