Amorim was dismissed last week, 14 months after his move from Sporting CP.
For Parker, the Portuguese's exit was always going to happen. He told Tribalfootball.com: "The owners employed Amorim, so have to take a considerable amount of the blame here.
"It’s so important to do your due diligence and I don’t think enough was done to ensure Amorim was the right man for the job. As it’s proven, he most definitely wasn’t the right man at all. Yes he inherited a squad from Ten Hag, but barely got anything out of the team whilst he was in charge.
"Refusal to change a system that didn’t work was one of those key things. But Amorim himself wasn’t up for the task at all. Not qualifying for Europe, struggling in the cup competitions and a style of football that wasn’t good enough. Losing a cup final as well where they didn’t play well.
"Yes, the signings had potential and you could see Cunha, Mbuemo and in recent games Sesko improving, but elsewhere it was never good enough."
Carrick will be good for Man Utd attack
On Michael Carrick's appointment to the end of this season, Parker believes United's attacking will benefit from the former Middlesbrough manager's approach and tactics.
He said, "Firstly I would say (Bryan) Mbuemo. He has really impressed as the season has gone on and it was a massive shame to see him head off to the AFCON. We missed him big time. But now he can come back, I think he can really work well under Carrick and continue to score plenty of goals and be effective where it matters most.
"The next player would be Amad. Young and hugely talented, I think Carrick can really get his confidence levels high and enable him to perform at a very good level. Create plenty of chances and also contribute with goals as well. He needs to be fearless on the pitch and perform well and Carrick can get the best out of him too.
"Finally (Benjamin) Sesko. He is so important to the team going forward now. The talisman up top and Carrick can also give him a big confidence boost by making him the main man and enabling him to work well with Mbuemo and Amad to contribute to Man Utd’s goal tally."
Paul Parker was speaking to Tribalfootball on behalf of Betfree