Tony Lloyd was responding to the UK Statistics Authority's findings that policing faces a £160m real-term cut in funding in 2015-16 and 2016-17.
The figures are in apparent contrast to Mr Osborne's Spending Review pledge.
A spokesman for the Treasury said they "completely reject any suggestion the public had been misled".
Mr Lloyd, who is also Greater Manchester's police and crime commissioner, said the Authority's findings had called the chancellor's promise into question.
He said: "This analysis exposes the weakness of the chancellor's pledge to protect local policing, after years of cuts, and is an embarrassment for him and the government.
"I have said from the start that this is still a 'cuts budget'. This year we face a cut of £8.5m cut from our budget. That's on top of the £180m already cut from GMP and the 2,000 police officers that have disappeared from our streets.
"To try and make the sums add up I have had no choice but to ask local people to contribute more to maintain their police service, but the additional £3.5m raised from council tax is still not enough to meet the shortfall as we try and find savings of £70m.
"The Chancellor needs to redo his sums and make good on his promise protect our police service."
The Treasury said the widely reported comments by Sir Andrew Dilnot, the chairman of the UK Statistics Authority, do not provide the full picture and exclude elements such as the police precept.
A spokesman said: "The government has been completely clear that we are committed to funding the forces that keep our country safe, which is why we have protected overall police spending in real terms with an increase of £900m cash by 2019-20 to maintain strong frontline policing.
"This is on top of an extra £500 million extra funding for the counter terrorism budget."
Greater Manchester's mayor has called for Chancellor George Osborne to apologise for "wrongly claiming there would be no cuts to local policing".