Amoo's contract was not renewed by the club at the end of last season, in a reorganization that saw the team disbanded, then reconstituted with less than a week to kickoff of the new season.
Allen, his replacement, was fired on Monday after a dreadful run which saw them pick up just 17 points from 16 games, but Amoo says the club must look higher for a solution to their problems.
"For me, the issue with 3SC is not coaching. With the way things are today, maybe Allen should not have jumped into that door," Amoo told KickOffNigeria.com.
"I'm not putting up a defense for him even though he is a colleague, but 3SC's problems is more than Allen.
"They have not dismantled the bottlenecks in the club. We have to look at it from the angle of who leads the team in terms of administration. What experience and exposure do they have? There is a lot of politicking in Nigerian league, and you must know it to win.
"You have people like Taiwo Ogunjobi, Felix Anyansi, Mike Idoko, Fatai Olayinka who have a lot of experience in the league.
"The coach must have a sound administrative set-up to support him, otherwise it will be tough.
"If you don't have people like that, you will find it difficult even to have control of the players. And 3SC, I am sorry to say, did not have that. Although I don't know about the new board."
Former international Mutiu Adepoju was at the helm when Amoo coached 3SC, and the coach said although Adepoju did his best, he was not in the same class as the names he mentioned.
"Mutiu tried his best, but talking as an insider, he needed to do more than what he did. By the time you take one of those I'm talking about, you will see a big difference.
"You can't compare Mutiu with someone like Idoko, or Ogunjobi or Anyansi. These are people who know all the intricacies of the Nigerian league. Mutiu is coming up good, but he needs more support."
Amoo gave examples of where administrative naïveté cost Shooting. "I remember when 3SC won a clear, genuine protest. And before we knew what happened, things had changed.
"Or when other teams will tell you they cannot play certain games because certain conditions have not been met. But 3SC cannot try that.
"3Sc cannot tell you we don't want this match official. But other clubs do that. They will put reasons and make a case, but 3SC cannot do that."
He also suggested that having football outsiders with little knowledge of the system could have been a factor. "Look at teams like Dolphins, and Ocean Boys when they won the league. The people running the clubs did not just come from outside. They were within the Nigerian league and understood the intrigues. And they had good financial backing which 3SC did not have.
"There were times when the players would say they don't care. And I told them they had to care because we had our names and we had our reputation to protect.
"As a coach, it is never good when your management puts you in a position where you have to beg players to play. It undermines your authority. And that is not good."
But Amoo praised the 3SC fans for their support. "A lot of people say 3SC fans are a problem, but I don't agree. Fans are not the problem. They are the ones you need to succeed. They are always behind the team. No fan has always tried to influence the players I tried to select.
“Infact, the fans make it easy."