Instead, Birmingham College of Food and Sutton Coldfield FE College must repay Pounds 2 million which, the council insisted, it was owed by the colleges in outstanding debts when they became independent in 1993.
But the judges, whose decision followed a three-year battle, in a unanimous decision said Birmingham City Council had to shoulder substantial blame because of inadequate accounting.
The colleges denied owing money which the council insisted was spent on their behalf between 1990 and 1993. They went further when they took the case to the High Court in 1994, arguing that they were each owed Pounds 7m in European Social Fund grants which the council had failed to pass on.
The High Court supported the colleges but the Court of Appeal found against them "with regret". The colleges are now seeking leave to appeal to the House of Lords.
The Euro cash was targeted at improving education and training in depressed areas of the West Midlands. The principals claimed that it had been earmarked for their colleges and should have been passed straight to them.
Eddie McIntyre, principal of Birmingham College of Food, Tourism and Creative Studies, said he was "very disappointed". He added that many colleges, already reeling from the effects of Government budget capping this year, were in no position to cut back further.
"It would have been extra money that we would have been able to spend on our students," he said.
His college must now pay the city council Pounds 1.7 million. Sutton Coldfield must find about Pounds 225,000.
Lord Justice Leggatt, presiding, criticised the council. There was no dispute that the council had received more in European cash than it had passed on to the colleges in the years 1990-93, he said. But it had operated within its budget and both colleges were liable to repay the deficits.
"I reach this conclusion with regret because the council does not appear to have made any effort to provide the colleges with figures showing what became of the excess of the actual grants.
"On the face of it those extra sums went into the council's coffers, whereas if they had been paid over to the colleges, they would not have been in deficit."
The law did not absolve the council from blame for failing to reveal where the excess went, said Lord Justice Leggatt.
He added: "It is extraordinary that litigations designed to elicit answers in principle could have been allowed to proceed without the council divulging actual figures or explaining accounting treatment.