Bryan Mbeumo had given United a first-half lead, but Spurs struck late to lead 2-1 before Matthijs de Ligt's 96th minute equaliser.
Afterwards, Amorim lamented: "During the game we felt like the three points were there to take home. But then with everything that happened, Harry Maguire and Casemiro coming off and conceding two goals... we scored again and it's a point.
"When you cannot win you don't lose, once again we did that. We have so much to grow as a team, because today was our day to win this game.
"We need to look at ourselves, we were not pressing with the same intensity, we felt comfortable but we need to understand that if we had more bravery we kill the game. But sometimes this happens, you have a better first half than second.
"We believe in our capacity to score goals until the last minute."
On the performance of goalkeeper Senne Lammens, Amorim said: "He is doing really well, he understand in a game a lot of things can happen, but as a goalkeeper you have to move on. It's a like a new game every time the ball is on the pitch.
On concerns over Benjamin Sesko's late match injury, he also said: "We have to see, we think he has a problem but let's see.
"It's a little frustration, but also pride at the response of the players at the response to second goal of Tottenham.
"This is the tip of the iceberg, we are at the beginning of becoming a strong team, so we have a lot to do."