She also suggested that Prime Minister Manmohan Singh's address to the nation on the December 16 incident could have come a little earlier instead of a week after the "horrendous" crime.
Dikshit acknowledged that people "shy away" from helping others who are in distress because they feel that they will be "harassed" by the police, and asked the force to change its attitude and style of functioning. She felt that the force personnel should behave as "gentleman" police at the need of hour.
"It worries me. Yes. It worries me that police force is not as sensitive or responsive as it ought to be or well behaved as it ought to be... The systems need to be changed and judicial system needs to be changed and bureaucratic system needs to be changed but it has to be thought out. But please remember it is not going to happen tomorrow," she told Karan Thapar on Devil's Advocate programme on CNN-IBN.
"Fault lies with police. I don't know. I have not minced my words (in saying) where the failure of this has come (from). In fact, I have not overtly but covertly criticised this. It is not my job to appoint a Police Commissioner or take him away. It is the job of the Home Ministry and I am sure they will do something," she said in reply to a question on who was at fault for the incident.
Dikshit said such mass protests were a challenge to politicians, bureaucracy, judiciary, police and to everybody, while "fully sympathising" with the anger and anguish of the people.
Calling the gangrape of the paramedical student as "horrendous", she said the Supreme Court's observation that women in Delhi are not safe was "telling" and says it all.
The Chief Minister rejected suggestions that the government did not act swiftly to control the situation, saying it had moved fast in setting up fast-track courts and appointing the Justice J S Verma Committee.
In this context, Dikshit said the Prime Minister addressed the nation, while Congress President Sonia Gandhi and Rahul Gandhi met the protesters.
She also noted that Singh and Gandhi received the body of the girl, who died in a Singapore hospital on December 29, at the Delhi airport.
To a question on whether Singh's address came late, she said, "Maybe it was one week too late. He should have perhaps done it earlier."
"...It (the government) moved...to get some other things like we got this 181 line or whatever it may be a small effort, that rang the bell for everyone to wake up," she said.
Dikshit also asked why only politicians were being targeted and why not any other organisations, in an apparent reference to the Delhi Police.
"Why are you putting it all on the politicians? Why not on many other things... The society, the way we are bringing up children, the way we are teaching children and the way our schools are running. Why is it only the politicians?" she asked.
Pitching for a change in the system, she said the police needs to have more faith in the people and if they have faith as a police force in the people, people will have faith in it.
Asked whether she addressed the issues with Home Minister Sushilkumar Shinde and Police Commissioner Neeraj Kumar, she said she had met them and explained the issues and had even written letters to them.
Asked whether the Home Minister and the police understand the issues, she said: "Yes Yes. I hope they do. My understanding is amongst all these people, whether it is the Home Minister or the Police Commissioner or Lt Governor or Secretary, Home.
"They are not the people who are in touch daily with the people I am because I happen to be the Chief Minister."
Dikshit also said during her meeting with the Prime Minister, she told him that there should be an immediate change in the mode of police training if one wants to bring the confidence back into the policing system.
The Chief Minister also felt a lot of the VVIP security has to be removed, saying, "I can tell you about myself, I don't need that kind of security. Why?"
Asked whether she broached the topic with Shinde, she replied in the affirmative and quoted him as saying that there will be a review of VVIP security so that it can go to the people.
On the apex court's observation about safety of women in Delhi, she said, "Now you see the judiciary and no less than the Supreme Court had to come out with this comment. This comment is telling, I mean it says it all.
"Something I may not be able to say or somebody else may be saying and the Supreme Court is saying. This is about the third or fourth time that they have said something like this."
The Chief Minister said no one has any "magic wand" to bring back safety and that it will take time. She also said the family values where the boy is treated as a "king and the girl as a curse" needs to be changed first.
Dikshit also said her government would launch an awareness campaign called ‘Aawaz uthao, chintan karo' (Raise your voice and introspect).