Morgan Rogers scored two excellent goals for Villa, but the United boss was forced to re-shuffle his midfield after Fernandes was forced off at halftime.
"I think we were the better team today. We were unlucky, even with the injury of Bruno, but during the game even without him we were the better team," Amorim said.
"We did a very good job that no one is going to remember tomorrow, because what matters is the result."
The 40-year-old coach said Fernandes seemed to have suffered a soft-tissue injury and that there was no prognosis as to when he might return. Shea Lacey and Jack Fletcher, son of former United player Darren, were given their debuts.
"We need to prepare all the guys that we have for the next game, we cannot use anything as an excuse. No one is going to remember these problems, so let's cope with that. It will make us stronger," Amorim said.
United defender Diogo Dalot was blunt in his assessment of what the loss of Fernandes would mean for his side, who are seventh in the table on 26 points, 10 behind third-placed Villa.
"It's massive. We don't know how bad it is, but for him to come off, we know how tough he is. Hopefully, it's not too bad, and we keep with him for the next games," he said.
"This is the time that opportunities come for other players, and the time you step up and show you deserve to be in the team and play more minutes," he added. "We are Manchester United, and we have to find a way to win."