It's a misleading simplification. Profit motive (or "private sector") is not equal to efficiency. But it's a strong motivator for it. Not perfect though, and the further you are from getting outcompeted and dying, the more space you have for inefficiencies to creep in.
One of the big sources of inefficiency affects governments and companies the same - the difficulty of keeping an organization functioning grows superlinearly with the number of people in it. That's why in a small company, if your computer breaks, you can just borrow the company card and go to the nearest store to buy a new one, while in a large company, you'd be dealing with procurement and five layers of management approvals. A large company looks not quite unlike a government organization.
(Also worth mentioning that absolute efficiency is not a good thing either, when it comes to dealing with people.)
But a government has (self-imposed) financial constraints as well.
Besides, if you decide mostly or only based on financial constraints and not based on reason and good ideas then you should not be in the position to decide what to do.
Resources might be wasted on purpose to avoid tighter financial constraints in the next year that takes into account the spending of the current year.
One of the big sources of inefficiency affects governments and companies the same - the difficulty of keeping an organization functioning grows superlinearly with the number of people in it. That's why in a small company, if your computer breaks, you can just borrow the company card and go to the nearest store to buy a new one, while in a large company, you'd be dealing with procurement and five layers of management approvals. A large company looks not quite unlike a government organization.
(Also worth mentioning that absolute efficiency is not a good thing either, when it comes to dealing with people.)