Healthcare Improvement Scotland said several senior charge nurses and clinical service managers across three wards raised issues during an inspection visit.
NHS Grampian was asked to supply an improvement action plan.
Senior inspector Ian Smith said the action plan had given "assurance".
He added: "We will continue to follow this up with NHS Grampian on future inspections."
The inspection visit took place in April, as part of Healthcare Improvement Scotland's programme of inspections on the standard of care for older people in acute care in Scotland.
It was to check that older people were being "treated with compassion, dignity and respect".
NHS Grampian was said to be "performing well" in a number of areas.
An NHS Grampian spokesperson said: "We welcome this positive report which highlights the many examples of good practice in the care of older people in hospital, particularly the compassion, dignity and respect with which our patients are treated.
"We are also pleased that 93% of the patients surveyed said that the quality of care they received was good, reflecting the warm and caring interaction observed by the inspectors between staff and patients.
"The areas for improvement identified in the report are already being tackled, and an action plan has been agreed.
"Although acknowledging that patient care was not compromised, the inspectors asked that staffing levels in three wards be addressed."
NHS Grampian is trying to improve staffing levels at Aberdeen Royal Infirmary after concerns were raised by staff.