Ramos broke the deadlock in the 69th minute, finishing a low cross from substitute Alexis Saelemaekers, before an unfortunate Redouane Halhal own goal, deflected in off a shot from fellow substitute Ardon Jashari, sealed the points in the 89th minute. The match, Amorim's home bow as Milan boss, was preceded by a tribute to club great Franco Baresi.
Amorim was pleased with the result but pointed to defensive work still needed.
"Conceding all these chances means that sooner or later we're going to concede a goal, and at that point it becomes difficult to turn the situation around. But it's our current way of defending - we leave a lot of space, and it's hard for my players," he said.
"Sometimes, while we're attacking, it's difficult for them not to just watch the ball, but to think about what to do if we lose it.
"These are all details we need time to work on. Right now we're defending in a completely different area of the pitch, with half the pitch left totally open and often in one-against-one situations."
He added that the team still has plenty to improve, even in victory.
"The idea I've formed during the game is that we're doing a lot of good things, but there's still a lot to improve to become a really strong team," Amorim said, explaining he heads straight to the dressing room after full time to compose himself before facing the media. "I need those five minutes for myself... I was really proud of the players, because they're showing courage and working hard."
On summer signing Gonçalo Ramos, Amorim praised his composure after two earlier missed chances before he scored: "This is where you see great players... he didn't dwell on the earlier misses. That's a quality that comes with experience and quality. So I didn't say anything to him - I already knew that on the next chance he'd score."
Venezia FC coach Giovanni Stroppa was proud of his side's display despite the defeat.
"It was good, but it's not enough. We need to do more. I'm satisfied, but as last Sunday, everything you do with a positive performance makes you believe in it," he said. "We had a couple of chances in the opening minutes. But we produced a lot of good content at San Siro against this Milan side - I'll take the performance and the work we're doing."
Asked how he keeps the squad united after back-to-back defeats, Stroppa added: "We're at the start. It's a process. There are plenty of positive signs to be optimistic about. We need to work on certain aspects - the second goal we conceded really bothers me."
On the tribute to AC Milan legend Franco Baresi before kick-off, Stroppa said: "He left me a great deal - he was an incredibly important figure, both professionally and as a friend. Inside the dressing room, privately, he was always unique. Not just for the armband he wore, but for the person he was. Unique."