The prohibition order from the Health and Safety Executive (HSE) only applies to NHS Greater Glasgow and Clyde, where the deaths occurred.
Scottish Liberal Democrat health spokesman Jim Hume MSP said there were "clear implications" for elsewhere following the action in the wake of deaths at Stobhill Hospital in Glasgow and Dykebar Hospital in Paisley.
Mr Hume said: "Our universal health service means that all mental health patients and their families should expect the same level of care regardless of where they are being treated."
He called on NHS Scotland to consider whether plastic bin bags should be banned in mental health facilities across the remaining 13 Scottish health boards.
Mr Hume said: "I know NHS boards, responsible for managing their own procedures, will want to work quickly with all relevant partners to ensure any lessons are learned. We need to ensure any issue around mental health care is resolved just as quickly as any other problem on our health boards."
Meanwhile, NHS whistleblower Rab Wilson has warned nurses on hospital mental health wards are spending too much time on paperwork and not enough on protecting patients.
Mr Wilson, a former psychiatric nurse who fought a successful six-year battle to expose serious incident reports at NHS Ayrshire and Arran, said the use of risk assessments was a box-ticking exercise that got in the way of work with potentially suicidal patients.
"There has been a proliferation in the creation of psychiatric self-harm risk assessments that have to be completed by very busy frontline medical and nursing staff," he said.
"Completing one can easily take up an hour or more of a staff nurse's time. Time that may paradoxically be more useful spent in observing the actual patients in order to prevent incidences of self harm."
In a letter to the Herald, Mr Wilson added: "The reason these risk assessments are completed may have more to do with the 'box-ticking' culture in our NHS and the need to protect those at the top from shouldering any responsibility or accountability whenever another suicide happens.
"Removal of black bin bags from psychiatric hospitals will do little to prevent these tragedies. The freeing up of frontline staff may do more to save patient's lives."
In 2012 a patient committed suicide using a bin bag at Stobill, then last month a 27-year-old woman patient suffocated at Dykebar last month.
A Scottish Government spokesman said decisions about managing risk on wards were the responsibility of individual health boards.
He added: "Every suicide is a tragedy that has a far-reaching impact on family, friends and the community long after a person has died. Our thoughts and sympathies are with the friends and loved ones of the patients who have died in these tragic incidents.
"Individual NHS boards have responsibility for managing risk on their wards. However, we will be closely considering any advice we receive from the HSE on this matter. We are committed to working with Health Improvement Scotland to support improvements for boards that focus on areas of practice which make mental health services safer for people at risk of suicide."
Letters: Page 16