After enduring heavy criticism for his formations and tactics, United finally won three games in a row for the first time under the Portuguese manager who approaches his one-year anniversary at the club next month.
United sit sixth in the standings with 16 points after nine games, six points behind leaders Arsenal and a point ahead of reigning champions Liverpool.
"It was a journey, a big journey. It was really tough. Good moments, bad moments. I learned a lot, that is really important," Amorim told reporters ahead of Saturday's trip to Nottingham Forest.
"I learned that even in my lower moments I can stick with the thing I believe and that is a good thing for anyone to understand.
"Today, the answer is different from three weeks ago, so it is important to understand that. It is one of the big honours of my life to be here and I want to continue here for many years."
Amorim responds to Dyche dig
Forest are managed by Sean Dyche, their third manager of the season and one of Amorim's critics, with the Englishman saying earlier this year that the Portuguese would have won more games with a 4-4-2 formation.
"I always say that I have a way of playing that is going to take a while and then in the future it is going to be better," Amorim said.
"We don't know that. I can look at Sean Dyche as a manager and a pundit. If you are a pundit and you don't say very strong things, I don't want to watch you. I am the same. I can completely understand that it is a different job.
"I know Sean Dyche is smart and he knows how to play the game. He understands that there is one thing seeing the game and talking about it. It is another thing to coach a team."
Amorim said he was unsure if injured defender Harry Maguire would be ready for the game while Lisandro Martinez is not ready even though he has returned to full training after suffering an anterior cruciate ligament injury in February.