Mark Haysom, the Learning and Skills Council chief executive, told the Association of Colleges conference: "It's a real issue. It's striking how much people are talking about this."
His comments were based on the number of cases of under-funding which have been brought to his attention by individual colleges - although the national figure has yet to be worked out by the LSC.
Colleges are set recruitment targets for the year, which are tied to their budgets from the LSC. If they are too successful in attracting students, they either have to turn them away or fund courses at their own expense.
Many colleges use money raised from international students' fees and consultancy work to pay for unfunded students.
The shortfall in funding varies across the country, with some areas short of cash by 10.9 per cent, while others have a 5 per cent surplus.
The AoC estimated that, last year, there was a 2 per cent shortfall on the pound;2.6 billion budget for 16 to 18 education. That is equivalent to every college subsidising teenagers to the tune of pound;135,000, although many more students may have been denied places.
Mr Haysom said that unfunded places were increasing even though the LSC had budgeted for more than 5 per cent growth in some areas. "It's encouraging in one sense and concerning in another," he said.
The LSC had to put even more effort into understanding local demand and budgeting properly for it, Mr Haysom said.
Joe West, principal of Barnsley college, said he had to find pound;300,000 to fund 92 extra students last year.
Only an extra grant from the LSC after the college took over a work-based learning project enabled him to cross-subsidise the unfunded students and avoid a deficit.
He said: "I wouldn't say that they are deliberately exploiting us. But I do think the funding system is unfair.
"Government policy is to provide free education for 16 to 18-year-olds.
That should be done in a way which doesn't require subsidy from somewhere else."
Mr West said he expects a considerable shortfall next year as well. ""We feel there is a moral obligation if young people apply and are suitable for our courses to take them on," he said.