The Portuguese was axed on Monday after 14 months at Old Trafford after an explosive post-match interview following his team's 1-1 draw at Leeds on Sunday.
Under-18s coach and former United player Fletcher was put in charge for Wednesday's match at Burnley and faced the press for the first time on Tuesday.
The former Scotland international is expected to remain in place until the club appoints a caretaker boss, with United planning to name Amorim's permanent successor at the end of the season.
Fletcher, 41, said the past 24 hours at Old Trafford had been "surreal".
"It's an amazing honour to be able to lead a Manchester United team," he said. "I don't even think it was in my wildest dreams that that was something that could potentially happen, even thinking about playing for the club and stuff like that.
"But to lead out the team is an amazing honour and something I am really proud to do.
"It's not (happened) in the circumstances that I expected it to happen so that obviously is something that doesn't sit quite easy with me, but I just have to think I've got a job to do and I've got to lead the team tomorrow and think of the great honour and pride in doing that."
Fletcher said conversations with the club's hierarchy had focused on Wednesday's game against struggling Burnley and they would speak again after the match.
Fletcher, United's technical director between 2021 and 2024, was asked whether he wanted to try to earn the manager's job on a full-time basis.
"Honestly it's not something I've thought about," he said. "I'm focusing on Burnley. I think that discussion is for after the game.
"There has been that much going on and it has all happened so quickly that all my concentration, efforts and thoughts have gone into Burnley."