United seemed on course to make it four successive Premier League victories for the first time since February 2024 after Casemiro's first-half header at the City Ground, only for two Forest goals in two minutes to turn the match on its head.
Amad Diallo's stunning volley rescued United a deserved point which continued their improvement under Amorim, a year to the day since he was appointed manager.
"We lost control of the game for five minutes," Amorim said. "But my feeling is that the players tried, really tried. They tried during the week and they tried today.
"In the past, if we had this kind of bad five minutes and we suffered two goals, we didn't recover. Today is a different feeling. You can sense that we could not win this game, but we are not going to lose.
"That is a feeling that a big team sometimes has to have. Last season we lose that game, by more goals."
Victory would have moved United up to second in the standings - a long way from their final position of 15th last season.
"The confidence, of course, is completely different," Amorim added. "We came from three good games and we have a different confidence. We understand each other better.
"And a game is like that also. We have good moments, we score," he added. "You can sense that we have control of the game when the first half finishes. We start the second half and we suffer. We managed to recover from that and that's a good feeling."