Alphadjo Cissé had put AC Milan ahead in the 68th minute before Gatti, introduced as an auxiliary forward, equalised in the 92nd minute with a header from a Koopmeiners cross, sparking wild celebrations that briefly delayed Juventus getting the ball back to the centre circle.
The result kept both sides unbeaten this season, though it also opened up a small gap to early pace-setters Inter and Roma.
Amorim was refreshingly honest in his post-match assessment, conceding his side had not done enough to deserve the win their early lead had promised.
"We didn't deserve to win — if we're honest, I don't think Juventus deserved to lose. We tried to play our game, but we weren't good with the ball. There were moments when we controlled the game in the first half, but then, when we started losing a lot of possession, we suffered," the Milan boss said.
The Portuguese pointed to a lack of composure in simple situations as the root of his side's second-half struggles.
"We have the individual quality, what was missing today was the simple things: in football, the simple things are the best," Amorim said, before addressing questions over the club's approach to young forward Alphadjo Cissé.
"I want to be careful with our young players, because in football today there's a tendency to build players up too soon. He's a young lad at the start of his career. I'm really happy for him, but I look at Cissé and think he can do even better. The same goes for the others."
Luciano Spalletti, for his part, praised his team's resilience in fighting back from behind against a well-organised opponent.
"The intention is always the same: to affirm who we are. The opponent changes, the mood can help or not help. Personal issues can create doubts, but here you need Juventus-level character," the Juventus boss said. "We went into the game man for man throughout, the way Milan did too — a serious match. After conceding, we kept believing we could do it. Juventus didn't deserve to lose this game."
On the officiating around a contested contact between Kolo Muani and De Winter, Spalletti backed the referee's judgment.
"Mariani is one of the best Italian referees, and I think the line we're seeing applied is the right one. We're adapting to what happens elsewhere in the world," he said, before outlining what he wants to see improve.
"I'm asking for us to press and build serious things when we have the ball. The real difference is made in the moments nobody measures."