Rishi, 62, took to Twitter to share his resentment over no recognition for the "Junglee" star.
"Ponder. My only resentment is that Shammi Kapoor never got recognised by the government in his lifetime. Posthumously would be great but then I think I am being too greedy!," he tweeted.
The actor's tweet comes after his another uncle Shashi Kapoor was conferred the prestigious Dadasaheb Phalke Award yesterday.
Rishi also asked his followers and Shammi's fans whether they agree with his views.
Shammi, often called the Elvis Presley of India, died on August 7, 2011. He was 79.