The British public "don't simply resort to violent unrest in the face of challenging economic circumstances" and it is "ridiculous" to suggest that savings could not be made in the police service, she said.
Mrs May took to the stage after Chief Superintendent Derek Barnett urged her to protect the service from the worst of the cuts to ensure it is kept "sufficiently resilient" to be able to respond properly to "widespread disorder" on the streets.
It comes after the Police Federation predicted it would be "Christmas for criminals" if 25% budget cuts go ahead, leading to the loss of up to 40,000 officers and making it "inevitable" that crime would rise.
But Mrs May dismissed the concerns as "pure speculation", saying: "Lower budgets do not automatically have to mean lower police numbers.
"The front line should be the last place you should look to make savings, not the first."
And she added that more officers will not lead to less crime if their time is spent on the "pointless tasks of form-filling and chasing targets".
"As any experienced senior police officer will confirm, the effectiveness of a police force depends not primarily on the absolute number of police officers in the force but the way those officers are used," she said.
"The key to success is good management and leadership.
"We all know that there are efficiencies to be made in policing and it would be crazy to suggest that there aren't."
The Government wants to be the first in more than a decade to free officers to cut crime, giving them the space needed to do their jobs, she said.
"We are spending beyond our means and we cannot go on like this.
"We will help you by getting out of the way and stopping interfering in policing.
"You are the professionals in operational policing and we, the politicians in Westminster, have no business telling you how to do your jobs. Nor have civil servants in Whitehall.
"We won't burden you with a never-ending string of new initiatives. We won't impose national targets and one-size-fits-all solutions to local problems.
"Instead, we'll give you the space to do your job."
Speaking at the annual conference of the Police Superintendents' Association of England and Wales in Cheshire, Mrs May said the Government will cut red tape and slash bureaucracy in a bid to hand back power to the professionals and the people.
"That means getting your officers out from behind their desk and out on to the streets, where they want to be and where the public want them to be," she said.
"I want police officers to be crime-fighters not form-writers."
The Home Secretary told the superintendents they were "key to delivering reform" and urged them to "push partnership boundaries further" as they work with local authorities and others to achieve results.
She said it would also be necessary to look at police pay and conditions, and added: "There are no easy answers but I would really value your input."
Earlier, Mr Barnett urged Mrs May to ensure that officers feel valued as she oversees the most radical reforms to policing in 50 years.
When there is "widespread disorder on our streets", for whatever reason, it will be police officers who have to respond, he said.
"In an environment of cuts across the wider public sector, we face a period where disaffection, social and industrial tensions may, I repeat may, well rise and we have witnessed the growing sense of unrest at the TUC conference this week," he said.
"We will require a strong, confident, properly trained and equipped police service, one in which morale is high and one that believes it is valued by the Government and public."
The senior officers in the audience applauded the Home Secretary before she left the conference, but some said they were far from reassured by her speech.
Chief Superintendent David McDonnell, head of protective services in Suffolk, accused her of being "disingenuous".
In a question and answer session, Mrs May, who claimed savings will not necessarily mean fewer officers, told him she did not know the number of job losses yet.
"She is being disingenuous," Mr McDonnell said.
"I find it strange that she is saying she has no inkling as to how many officers will lose their jobs."
He also disputed the Home Secretary's assertion that the public will not resort to violent unrest.
"We have to look back to the civil unrest of the 1970s and 1980s and it would be foolish to assume that this won't happen again," he said.
"Our concern would be that we will not be sufficiently equipped to deal with it."
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