The Red Devils kicked off the Amorim-era with a 1-1 draw away at Ipswich to leave them 12th in the Premier League table.
United got off to a dream start after taking the lead just 81 seconds into the clash at Portman Road through Marcus Rashford.
The strike meant that Amorim became just the second permanent manager in Premier League history to see his side score in the opening two minutes of their first game.
But the visitors struggled to create anything of note after that, with Ipswich, who sit 18th in the table, taking control of the match.
And they got their duly deserved equaliser in the 43rd minute thanks to Omari Hutchinson's curler from distance.
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The Tractor Boys could have walked away with all three points had it not been for Andre Onana's heroics, with the goalkeeper twice denying Liam Delap form point-blank range.
United, who have won just four matches from their 12 top-flight matches this term, now sit eight points behind fourth-placed Arsenal.
And United icon Keane believes there is no chance his former employers will challenge for a Champions League spot this season - despite a change in management.
Giving his analysis on Sky Sports following the match, Keane was asked whether United have players that can consistently show their class, as opposed to moment of quality.
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To which he said: "No, and that's the big problem.
"This team, for the last year or two, has been all about moments.
"We saw with the first goal after the first minute, you think, 'A great start, a bit of quality, a bit of pace, a nice finish from Marcus getting into the areas you want him to be.'
"And then United just sat back and you're thinking, 'What are you waiting for?'
"Ipswich are a team near the bottom, obviously on the back of a good result from Spurs, but with their home record not great, go after them!
"It was if United almost were fearful of going on to win the game.
"The manager obviously made a lot of changes in the second half, and to be fair, you're thinking, 'He's obviously trying to win the game.'
"He's still trying to get to know these players, but United, the position in the league, their results, they probably lacked that confidence and belief.
"But do I believe this group of players have the quality to start getting Manchester United back up towards the top four/top five?
"I've been saying it for ages, absolutely not. The evidence isn't there.
"And again today, we've come down here thinking, 'A new manager, a new bounce,' and it's all very positive.
"But then when the game starts. It's the same old stuff. Predictable and a real lack of quality."
Next up for Amorim is a Europa League clash with Bodo/Glimt, before United welcome Everton to Old Trafford in the Premier League next Sunday.