He called for politicians to show greater support for the service, which has been beset by financial pressures and a series of scandals in recent years.
Mr MacAskill, who served as justice secretary from 2007 to 2014, made the comments as it was revealed chief constable Phil Gormley is being investigated by the Police Investigations and Review Commissioner (Pirc) over misconduct allegations.
It comes after the chair of police oversight body the Scottish Police Authority (SPA) resigned last month.
Andrew Flanagan quit the role following concerns over governance and transparency at the organisation, alongside criticism of his leadership.
While Mr Gormley is not being suspended from his role while the investigation takes place, Mr MacAskill said there is “a leadership gap appearing” within the force.
Writing for The Herald newspaper, he said: “The chairman of the SPA has resigned in inglorious circumstances and the senior Deputy Chief Constable, Iain Livingstone, is retiring.
“He was viewed as Mr Gormley’s likely successor but, with other senior officers going or gone, the leadership team is stretched.
“It’s time for the Scottish Government, which has distanced itself recently, to show greater support for the service and for opposition MSPs to cease grandstanding and political point-scoring.”
Mr Gormley was appointed as Scotland’s top police officer in January 2016.
He replaced Sir Stephen House, who resigned following a series of controversies, including armed policing and the M9 crash tragedy when a couple died after police failed to respond to reports of a car going off the motorway.
No information has been given regarding the nature of the complaint against Mr Gormley, but if a serious breach of standards is found, he could face dismissal.
In a statement released on Wednesday, he said: ‘’I am co-operating fully with the Pirc and will provide all necessary assistance to bring this matter to a timely and satisfactory conclusion.
‘’In fairness to others who may be involved, it is not appropriate for me to comment further at this time.
‘’I would like to stress that I remain focused on leading Police Scotland, ensuring that we continue to serve and protect the people of this country.’’