A "significant" number of fund management companies authorised to operate here before stricter regulations were introduced in 2017 have not yet fully implemented the new framework.
Some companies may face penalties, the Central Bank said today.
The Central Bank introduced the set of provisions over and above the minimum European Union requirements - its CP86 framework - to ensure the country's large funds industry had sufficient resources and controls to meet their obligations.
Among the 358 active firms reviewed, the regulator found that many of the longer established funds had only made limited changes and did not have appropriate levels of resources in place to ensure effective implementation of the framework.
The vast majority also had not appointed a chief executive, the review found.
This was contrary to Central Bank expectations that all but the smallest of fund management companies should have a CEO.
However the regulator said the new framework meant that the appropriate and effective overall levels of resourcing were in place for the large number of funds that set up an operation in Ireland as a result of Britain's decision to leave the EU.
The representative body for international investment funds in Ireland, Irish Funds, said it was confident that the recommendations would help the wide range of fund management companies to assess and determine any necessary changes.
The Central Bank has started supervisory engagement with funds where specific concerns have been identified.
For many, that may result in agreeing specific changes but the regulator said its "full suite of tools" was available for more serious findings.
Another industry-wide review will be held in 2022.
"Too many firms evidenced significant shortcomings," the Central Bank's Director General of Financial Conduct Derville Rowland said in a statement.
"The lack of attention to issues that affect good governance is unacceptable and raises serious concern for the Central Bank. It is particularly concerning in light of the increasingly complex landscape in which firms operate," Ms Rowland said.
"Firms should also note that this is not a one-off review. Assessing the implementation of this framework will form part of our ongoing regulatory and supervisory engagement and we will continue to challenge firms where we see weaknesses," she added.