Fayose also asked the FG to explain why a former Chairman of EFCC, Ibrahim Lamorde, who was accused of corruption by the Senate, is back in public service.
Following the sack of the Secretary to the Government of the Federation, Babachir Lawal and the Director General, National Intelligence Agency, Ayodele Oke, Fayose said the President's action was an afterthought.
On Monday, October 30, Buhari terminated the appointments of the two government officials over allegations of corruption against them.
Lawal was accused of violating due process in the award of N200 million grass-cutting contract of the Presidential Initiative in the North East (PINE).
Oke was sacked for his role in the N13 billion discovered by the EFCC in an Ikoyi apartment, which he admitted belonged to NIA for 'covert operations'.
The two had been suspended in April - their eventual sack on Monday followed months of outcry by Nigerians.
In a statement issued by Fayose's Special Assistant on Public Communications and New Media, Lere Olayinka, he said Buhari's action was as a result of pressure from Nigerians.
Fayose said, "The President only acted because of the outcry of Nigerians, especially over the fraudulent reinstatement of the former Chairman of the Presidential Task Force on Pension Reforms, Mr Abdullahi Maina.
"Enough of using probe panels to shield people accused of corruption in Buhari’s government. Rather, they should be arrested, detained and prosecuted by the EFCC as being done to others perceived as the president’s enemies.
"Once again, Nigerians have proved that the power of the president is not greater than that of the people who elected him.
"What Nigerians expected from a President who rode to power on the basis of integrity is a total cleansing of his government, not setting up a panel to investigate corruption allegations involving his men and reluctantly sacking a few of them because of public outcry."
The Governor, who is one of the most consistent critics of the Buhari administration, also demanded that the report of the Vice President Yemi Osinbajo panel that investigated Lawal and Oke should be made public.
"Nigerians are interested in the full details of the report on the $43m discovered in an apartment at Osbourne Towers, Ikoyi, Lagos. The report should be made public.
"They also want to know what happened to the Minister of State for Petroleum Resources Ibe Kachikwu’s allegation of award of $25bn contracts without following due process against the Group Managing Director of the Nigerian National Petroleum Corporation, Dr. Maikanti Baru.
"Nigerians are interested in the report of the panel that looked into the Department of State Service report that indicted Acting Chairman of EFCC, Ibrahim Magu of corruption," he said.
He also said the APC-led government should explain why the former Chairman of EFCC, Ibrahim Lamorde, who was accused of corruption by the Senate, is back in public service.
Lamorde, who was unceremoniously removed from office, is said to be serving as the Commissioner of Police in charge of the Special Fraud Unit, Ikoyi, Lagos.