Whatever the decision of management, such decisions shall be final and binding on all employees in the company, and employees cannot question such decisions and/or resort to non-cooperation. However, an aggrieved employee can approach the HR department, and it is the duty and responsibility of the HR department to pacify them in a manner that leads to the employee finally accepting the decision of management.
The actions/reactions of a non-promoted employee are quite natural in a work environment because they are losing the freedom they were enjoying before, especially when interacting with a promoted employee. The non-promoted employee now has to follow certain protocols which they did not have to adhere to previously. Therefore, resistance on the part of the non-promoted employee is quite natural, and it is the duty of HR to convert that 'resistance' into 'support.'
In a home environment as well, if one child receives something extra, perhaps for their achievements in examinations, from their parents, the other child may feel unhappy, jealous, and show hatred towards the favored child. Parents, who understand the nature of both children, should console the child who did not receive the gift, and after a few days, such feelings will disappear from the other child's mind.
Here, in this context, HR should act like the role of a "parent."
Company policies need not be circulated to employees, but the information can be passed on to employees.