Marco Silva made nine changes from Benfica's previous outing, a gamble that paid off through his players' response rather than any special motivational push.
"When you change nine players from one game to the next there are always big risks, whatever the competition," Silva said. "Motivation-wise it was less of a factor, because in a game like this motivation is sky-high regardless — there was much more tactical work to do, and from that point of view the players were brilliant."
Silva credited an early goal, along with tweaks to his side's shape without the ball, for settling his changed line-up.
"Scoring straight away gave us the confidence and calm to approach the game differently," he said, adding that his side had been solid without conceding much before tiring in the closing stages as several players made their first appearances of 90 minutes for some time.
For Amorim, the damage was done by a mentality that unravels whenever AC Milan concede first.
"There was a problem in the first half against Lazio too: we go completely into panic mode when we ship the first goal," he said. "We need to stay calmer, keep our organisation and show a different energy. It's not just a lack of energy, it's about organisation, quality on the ball and understanding the moments of the game.
"When you concede, you have to keep the ball rather than throw men forward with no tactical plan. We lose our identity the moment we go behind."
Amorim pointed to a bright opening to the second half, in which Milan pushed Benfica back and created chances through Koni De Winter, before a second goal undid the good work.
"That second goal, on another transition where we took too long to win the ball back, cut our legs from under us," he said. "It wasn't the best possible European debut, but there are other games ahead. We can't change today's result, but we can change the next one."
The Milan coach conceded Benfica had simply been the better-organised side.
"If we look at the two teams, I think Benfica were more organised in what they wanted from the game, while we weren't able to do the same," he said, adding that the pressure of a big club was nothing new to him and that he was "always worried," win, lose or draw. Silva, by contrast, savoured a landmark night in front of more than 5,000 travelling supporters, while stressing his young squad still has "many battles ahead."