Amorim began his tenure at Old Trafford with interim predecessor Ruud van Nistelrooy having put together a four-match unbeaten streak before his arrival.
Within two minutes at Portman Road, that encouraging form had continued with Marcus Rashford putting United into an early lead, but that is as good as things would get for the visitors.
Omari Hutchinson's long-range effort got the Tractor Boys back on level terms and United were reliant on the outstanding Andre Onana to keep out further efforts from the home side.
Although Amorim may be relatively content with a share of the spoils in his first game, the Portuguese was not shy in publicly criticising two of his players for their decision-making.
Zirkzee failed to make an impact after being introduced as a 68th-minute substitute, while centre-back Evans was withdrawn after just 56 minutes.
Amorim disappointed with decision-making
After the game in East Anglia, the former Sporting Lisbon boss claimed that the duo - as well as other players - were making decisions that should be second nature to them at this level of football.
Speaking to Sky Sports, Amorim said: "Decision-making is a concern; you don't need to coach them [that] at this level.
"You have to keep the ball and know the momentum to put the ball in front. Sometimes you feel that you can't keep the ball and you have to put the ball in front.
"Then you have [situations] like at the end of the game [when] we were around the box with two strikers. Josh [Zirkzee] has to understand that he has to go to the box to help the crosses.
"So we are doing some things that were not at the right moments, which we have to address. The 3-4-3 is not the concern; the understanding of the game is what we have to improve."
On Evans, he added: "If you see the first half, you can see that they were a little bit afraid. Sam [Morsy] was always alone. We have to jump on him.
"Hutchinson was always in the dead space; Jonny Evans should be pressing his guy, but when we don't have the training.
What next for United?
Amorim's first fixture at Old Trafford takes place on Thursday night when Bodo/Glimt are the visitors in the Europa League.
Three days later, United play host to Everton in what will be regarded as a must-win fixture as they bid to climb the Premier League table.