Montella was without a number of first-team regulars at the Stadio Olimpico, with the likes of Alessio Romagnoli, Mattia De Sciglio and Giacomo Bonaventura all out injured while Gabriel Paletta and Juraj Kucka were suspended following their dismissals in the 1-0 win at Bologna last week.
It looked as though Milan were set for a fifth defeat in six matches as Lazio led through Lucas Biglia's first-half penalty, but with five minutes to go Suso found space between three defenders in the box and curled home a delightful equaliser.
"I'm much happier with this match than others where we got the same result," Montella told Premium Sport. "I'm increasingly proud to coach these players, who showed an incredible team spirit.
"Every coach has his own analysis. There are many times where I've said that we played better than the other team and then lost.
"The team used every ounce of energy that we had after Bologna, and we've had better days in terms of quality but this squad has made me emotional because of the effort they put in.
"It was a very difficult game, it wasn't that we got our approach wrong. The whole left flank had never played together, as well as three of the four in the centre. The team is stronger than anything."
Lazio defender Stefan de Vrij, meanwhile, felt dropping two points at such a late stage in the game was akin to having suffered defeat.
"This feels like a loss," he said. "We dominated and created a lot of chances, but we didn't close the game out.
"We lacked a goal, it's not as though they had loads of chances.
"They had two shots and scored one goal, [Gianluigi] Donnarumma pulled off some miracles. Unfortunately that's football."