The President and Vice President besides leaders of several parties, including Congress chief Sonia Gandhi, paid floral tributes to the former Prime Minister at Vijay Ghat.
Modi took to twitter to offer his salutations to him but did not go to his memorial.
"It is unfortunate that Modi did not pay homage to Shastriji at Vijay Ghat which is very close to Raj Ghat where he paid tributes to Mahatama Gandhi today", Congress spokesman Ajay Maken told reporters.
Asking the Central government to celebrate Shastri's birth anniversary as done to remember Gandhi, he talso ook a dig at Modi for not turning up at Vijay Ghat.
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"I also got to know that Prime Minister did not visit Vijay Ghat. I feel that ignoring Shastri Ji is not right," he said in a tweet.
Hardik Patel, who has been spearheading a movement demanding quota for Patel, accused Modi of insulting Shastri.
"It is very sad that he (Modi) did not turn up here. He has insulted (late Prime Minister) Shastri (by not visiting Vijay Ghat). Today is the birth anniversary of both Gandhi and Shastri, but people have forgotten Shastri," he said.
Shastri's son and Congress leader Anil Shastri downplayed Modi's non-participation but noted that it was for the first time that the Prime Minister did not pay homage at Vijay Ghat.
"It is Prime Minister's choice whom to pay homage and whom not to pay homage. He could be genuinely busy. It was a few minutes drive from the Raj Ghat", he said.
He suggested that the his non-participation could be linked to his government's decision last year to not hold anniversary functions relating to former prime ministers and instead asking concerned families and parties to do so.