"Those second-year decisions come beyond this term of Government and we will take those decisions when [they're in front of us]."
But the Herald understands Labour is now re-evaluating the rollout of the next stages of the policy.
Robertson said the scheme remains Labour Party policy "until it's not".
Asked if was ruling out implementing the policy in the second year, Robertson said he was not "playing the not ruling out game" for 2021 just yet.
"What I'm saying is it's still our policy – but clearly we want to make sure whatever we do in the vocational, post-school tertiary education space is appropriate for the future and those decisions will be made closer to the time."
Robertson also attempted to play down the significance of the reallocation.
He said when the fees-free policy was set up an assumption was made that it would lead to a 15 per cent increase in enrolments in the first year.
"That was always a generous assumption," he said.
"When you have a period of time where unemployment [is] very, very low, that traditionally coincides with lower enrolments, particularly in polytechs."
National's tertiary education spokesman Shane Reti said Robertson's reallocation showed the policy was a failure.
But Robertson disagrees.
"Far from it," he said when asked if the scheme was a failure.
"This is simply a recognition that not all of the money that was allocated for it was being used.
"Now we have the opportunity to put that towards what I believe is really significant shift in New Zealand's education system towards a vocational education system that's delivering people with the skills that they need."
National's finance spokeswoman Amy Adams was critical of other parts of Robertson's speech too.
"Mr Robertson said today that his wellbeing approach 'is about stepping out of the silos of agencies and working together to assess, develop and implement initiatives to improve wellbeing.'
"He went on to say that 'a wellbeing approach means looking at intergenerational outcomes. We have to think about the long-term impacts on future generations at the same time as meeting the needs of the present.'
"This is the very definition of National's Social Investment Approach. National's 2017 Budget saw the most rigorous investment criteria ever used to ensure funding went to evidence-based proposals that delivered long-run benefits for vulnerable people."