The Milan head coach was frustrated to see his side only perform in the second half in Turin on Monday, despite an impressive comeback that saw them rescue an unlikely point.
Torino were rampant in the first half - Andrea Belotti and Marco Benassi scoring - but Adem Ljajic then had a penalty saved by Gianluigi Donnarumma.
That gave Montella the opportunity to rally his players at the break and Milan were level by the hour mark thanks to Andrea Bertolacci's strike and Carlos Bacca netting a penalty of his own.
"I don't like to speak publicly about private matters, so what I said stays in the dressing room," Montella told Sky Italia when asked about his half-time words.
"After this match the team has learned another little lesson that will serve us well going forward. We saw many games and two or three Milans. It really was an indecipherable game at times.
"Torino deserved to take the lead and had a better mentality at the start. But we raised ours in the second half and deserved to go level.
"Towards the end it was wide open with either side able to get the winner. The plan is to play a full 75 to 90 minutes like this. If we can do it for 20 minutes, we can do it for a whole game. It is an issue of mentality.
"I want Milan to improve the approach and get games locked down in the first half, not the second."
He also hit out at substitute M'Baye Niang for failing to reach an Ignazio Abate cross as Milan chased a late winner.
"I did get rather angry with Niang at the end, as that move could have been finished," Montella said. "Niang needs to do more and put the effort in. Let's just say I complimented him many other times, but not this time."
The match was played as Milan, who are fifth in the table ahead of Saturday's home match with Napoli, confirmed the sale of forward Luiz Adriano to Spartak Moscow in a move reportedly worth just €1million.
The 29-year-old, who joined from Shakhtar Donetsk in 2015, has signed a long-term contract with Spartak after falling out of favour at San Siro under new boss Montella, leaving the Serie A club keen to get him off the wage bill.
"The club wants to thank Luiz for his two seasons in our colours and wish him the very best of luck for the future," Milan said in a statement.