"It's likely that tens of thousands of New Zealand still don't know they have been underpaid," Mr Clark said.
When challenged on the scale of the problem in Parliament, Mr Joyce blamed Labour's changes to the Holidays Act in 2003, which had made payments more complicated.
Mr Clark said National had been aware of the problem for six years and had failed to fix it.
The National-led Government formed a working group of unions and businesses to resolve the issue in 2010.
Asked why the pay was still being miscalculated six years later, Workplace Relations Minister Michael Woodhouse said the working group was unable to reach a consensus on how to simplify payments.
As a result, some employers were still struggling to calculate workers' holiday pay.
Mr Woodhouse resisted calls from Labour for a law change, saying that it was difficult to do so without reducing pay entitlements.
In the meantime, workers who were worried that they had missed out on pay should contact the Labour Inspectorate, he said. The inspectorate was also carrying out proactive audits.
What is the problem?
Holiday pay can be calculated two ways. It is either based on ordinary weekly pay at the start of the holiday or on average weekly earnings over the year. Employers must pay the higher amount to staff, but have not always been doing so.
How many people are affected?
At least 24,000 people in the public and private sectors have been underpaid between $70 and $1800. MBIE and New Zealand Police are two of the departments affected. The Government expects more cases to crop up.
How do I find out if I am have been wrongly paid?
Immigration Minister Michael Woodhouse says any concerned workers should contact the Labour Inspectorate.