The Bollywood veteran spoke out on Twitter after the three blasts in Mumbai on July 12.
He tweeted: "Each one of us will have to become a 'policeman'... look, notice, observe, feel, sense the danger in every step and report.
"Yes, the security forces will always be needed, but when vulnerable, let each one of us know that we are being watched and monitored.
"Let there be private or state professional units that take up the job of training citizens in anti-terror acts... make it compulsory."
The actor joined other stars in condemning the attacks on the Bollywood capital this week.
Bachchan wrote in his blog that the city will remain "resilient" in the face of terror, but added that it was wrong to forget about the incidents too quickly.
His latest film Aarakshan is facing controversy because of its depiction of the Indian caste system.
Bachchan plays a college principal forced to reconsider his outlook when his daughter falls in love with a Dalit, played by Saif Ali Khan.
Watch the trailer for Aarakshan below: