Matteo Cancellieri and Tijjani Noslin put Lazio 2-0 ahead by half-time at the Stadio Olimpico, but Diego Moreira struck twice in the space of two minutes early in the second half, either side of substitute appearances from Yunus Musah and Christian Pulisic, to complete a stunning comeback and secure a 2-2 draw for Milan.
Gennaro Gattuso, in his first home match in charge of Lazio, said the second-half collapse came down to a physical and mental lapse rather than any tactical failing.
"I didn't touch any particular nerve. The credit goes to the players, the credit goes to the more than a thousand fans who waited for us at Formello and accompanied us all the way here. In my view, in the second half it was a problem of legs and attitude, we didn't have the strength to stay in the match.
"We suffered their substitutions and we got away with it, we were good at staying in the game and taking a point home," Gattuso said.
Gattuso also pushed back on suggestions that a place in Europe should be considered the club's minimum objective this season.
"It's not correct to talk about Europe. Our goal is to think match by match. What matters is always attitude, and we have to be good at continuing on this path," he said.
Ruben Amorim, whose Milan side had won their opening two matches before drawing with Juventus and now Lazio, described the outcome as two points lost rather than a point gained.
"Everyone at the stadium saw two different matches between the first and second half. For me we lost two points and that's frustrating, but the important thing is that the players see it the way I do, because I heard Gila's words and that pleases me. We're frustrated, we lost points today and in Turin," Amorim said.
The Portuguese coach admitted he could not fully explain the gulf between his side's two halves, despite making no changes to his starting XI at the interval beyond substitutions.
"We looked like two different teams between the first and second half, yet we're the same team because most of the players were the same. I can't answer that," Amorim said. "I'm not crazy, now it's easy to say I would have started with the second-half team from the beginning.
"But the way we approached the match changed completely from the first half to the second. I wouldn't change the lineup, but I would change the energy with which we approached the match from the start."