Council leaders accused ministers of delivering "a slap in the face" for local democracy over their tough stance against Westminster and Croydon.
But heads said more councils should have been forced to boost funding for schools.
Westminster was ordered to increase its budget after it proposed passing on less than 60 per cent of the extra money the Government intended for schools.
The Conservative-controlled council was targeted despite spending 10 per cent more than the Goverment says it should on education last year.
Labour-run Croydon disputed the Government's calculations and said that it was increasing schools' budgets by more than other authorities which had escaped sanction.
John Troake, head of Haling Manor school in the borough, said that he had "mixed feelings" over the Government's action. "We are delighted that more money will be passed on to schools but it is only a greater share of a finite cake.
"Croydon has lost out in changes to the funding system and that is the fault of the Government," he added.
According to ministers, 24 of the 148 English authorities will not pass all the extra money to schools next year, although six have been excused due to changes in the funding system.
The money must be passed to schools not retained by councils for central services.
Local authority leaders said ministers had not given them enough extra money to deliver the rise in budgets demanded. Thirteen authorities had been given targets for funding that exceeded their grant increase .
Croydon said it had already been forced to raise council tax by 27 per cent because it had received the smallest grant increase in England.