Nigerian football fans have questioned the president's move to suspend the national team from competitive matches following its failure at the World Cup.
Nigeria Football Supporters Club (NFSC) chairman Otunba Yisa Olatunde Basorun said the decision had been taken "in haste" and would not help the team.
But the former head of the Nigeria Football Federation (NFF) told the BBC that it was a "welcome development".
Nigeria now risks being banned by Fifa from all international football.
The world governing body's statutes strictly forbid any political interface in the national administration of the sport.
On Wednesday, the NFF apologised to "all football-loving Nigerians" for the country's early exit from South Africa, where they failed to win a game.
"No previous board has qualified Nigeria for all major tournaments internationally," the federation said in a statement, adding that officials wanted Swedish coach Lars Lagerbeck to remain at the helm.
A special adviser to President Goodluck Jonathan had earlier announced that he had "directed that Nigeria withdraws from international competition for two years to enable the country to put its house in order".
The president also planned an audit of the country's World Cup organising committee and promised to hold accountable any officials guilty of corruption, he added.
On Thursday, the head of the Nigeria Football Supporters Club said it was not clear how not participating in the next Africa Cup of Nations in 2012 would help select a team that would win the World Cup.
"We should go by asking the old players to leave, and probably bring in new players and play friendly matches so that we can groom the younger players," Mr Olatunde told the Reuters news agency.
"[The president's] decision is in haste, and I don't think it is better for our football."
However, former NFF chairman Alhaji Ibrahim Galadima told the BBC Hausa Service that the government was only doing what the fans had demanded.
"The Nigerian people want reforms carried out in the national football team following a string of poor performances by the Super Eagles in the past years. So it is only natural that the government acts according to the will of the people," he said.
"I feel the decision is a welcome development, but there is so much uncertainty about what is going to happen to the national football team in the next two years," he added. "Nigerians love football so much, so it's going to very difficult for them not to see the team not play."
Godwin Dudu-Orumen, a Lagos-based sports commentator, said he was confident the government would make changes to those in charge of the game in the country, "because the biggest problem Nigerian football has is poor administration."