Bachchan has been an ambassador for UNICEF's polio campaign since 2005, and was honoured for his contribution to the cause at a Rotary International event on Tuesday (April 17).
Speaking to journalists about Aishwarya Rai Bachchan and Abhishek Bachchan's daughter, he said: "The little granddaughter was given a dose of polio two days back, in my presence.
"We must [make sure] that there are no polio cases for three consecutive years... we have just crossed one year. I feel we still have a long way to go. As a parent, I can only ask you, request you and get angry on you to continue this very noble cause."
Bachchan added: "I am happy that my 'angry young man' act campaign for polio has gone down well with the masses... We always have to ensure it does not re-penetrate [society] again.
"One should not treat this as a frivolous operation. We all have to continue working towards eradicating polio completely."
One case of polio was reported in India last year, according to UNICEF stats, compared with 41 in 2010.