He also said that "It took them 25 painful years to emerge out of the scandal despite their innocence."
"When my family and I were loaded with the accusations of the Bofors Scandal, they painted every aspect of our existence with the darkest colours ever... 25 years later, the prosecutor on the event, makes public the truth - the name of the Bachchans were 'planted'!! 25 years later...!!," he wrote in his blog.
Mr Bachchan, 73, feels accusations are easy to make in the age of technology, and people don't always bother to check facts.
"Controversy has the speediest vehicles .. and the belief in them, with the conveyance of the trillions of content through delicate fibres under the sea, or above through the satellited skies, an unstoppable desert storm that blinds not just the eyes of vision, but destroys the very foundation of civility and space..."
The Swedish whistle-blower in the case gave Mr Bachchan a clean chit in 2012 but the actor said he had to live under the burden of "deceit and lies" for a long time.
"When it is disclosed, they ask me for my reaction! What reaction may I give... What does one say... Who does one say it to... Can they wipe away the pain of 25 years... Will they be able to diminish the tainted colour of defamation..." Bachchan wrote.
(With inputs from agencies)