The figure emerged in a briefing paper from the Scottish Funding Council detailing how money is allocated around the country's colleges.
Colleges requested an extra £12m in 2013, but received just £7.1m, leaving £4.9m of demand unmet, it revealed.
Gordon Maloney, president of the National Union of Students (NUS) in Scotland, said: "These figures are extremely worrying news for Scottish college students.
"Not only is there a £4.9m shortfall in bursary and childcare funding - even after additional funding was provided through the last Scottish Budget - but demand for this vital funding has also doubled in the past year, without the cash there to meet this."
The NUS welcomed "continued protection" of further education student support, but said politicians need to come together and make sure the necessary money is provided.
"Additionally, there needs to be real and genuine reform to the system, with students knowing what they are entitled to, and their funding guaranteed, before they even set foot on a college campus," he said.
Liam McArthur, the Scottish Liberal Democrat education spokesman, also went on the attack, blaming Scottish Government funding cuts to the further education sector.
"When Liberal Democrat MSPs raised this issue with the Education Secretary, answers there came few," he said.
"With students now at his door, Education Secretary Michael Russell cannot continue to dodge the growing frustration towards his college cuts."
A Scottish Government spokeswoman said it was "committed to funding students in line with the NUS call for them to have money in their pockets".
He added: "For the next academic year we have provided protection from inflation for further education student support, despite substantial cuts to our budget by the UK Government.
"The total value of college bursaries package will rise to a record high of around £105 million ensuring that college students are better off and able to fulfil their potential as they progress their studies."