The Red Devils secured a 2-0 win over Aston Villa at Old Trafford in their final Premier League game, finishing 15th after their recent Europa League final loss to Tottenham Hotspur.
Under the Portuguese coach, United have won only 17 of 42 games and lost 17, marking a historically poor season for the Red Devils.
"First of all, I want to apologise for this season... I know it was really hard to support us in many games, but now we have to make a choice or we stay stuck in the past. Because this season is in the past, it's over,” Amorim said.
“We fight each other, or we stick together and move forward. Six months ago, in my first three games in charge with two victories and one draw, I said to you: 'the storm is coming'.
“Today after this disaster season, I want to tell you: the good days are coming. If there is one club in the world that proved in the past that it can overcome any situation, any disaster, it's our club.
“It's Manchester United Football Club. Now, I want to say sorry also to my players. Sometimes I was not fair, but I tried always to be honest with you guys. Thank you very much, see you next season."