The 80-year-old pontiff arrived in Myanmar on a six-day trip that will also take him to Bangladesh.
The church leader said a year ago that he would "almost certainly" visit India and Bangladesh in 2017 and diplomats said protracted negotiations were held on the itinerary.
India was finally dropped from the schedule without any official reason given by the Vatican or the Indian government.
"The Pope is coming close by and is not coming to India. As an Indian it hurts me as I am sure it hurts all Indians," Bishop Theodore Mascarenhas, secretary general of the Catholic Bishops' Conference of India, told news agency AFP.
"The Pope would have come as a messenger of peace, bringing a sort of a balm to the people."
India's Cardinal Oswald Gracias told the US National Catholic Reporter in July that finding a time that aligned with Prime Minister Narendra Modi's schedule had proven "a little bit of a difficult situation".
The last papal visit to India was by Pope John Paul II in 1999.
Christians -- overwhelmingly Catholic -- are the third-largest religious group in India after Hindus and Muslims.
The Indian Express newspaper on Monday quoted the Archbishop of Nagpur as saying that a papal visit "would have been a great boost for the country's image in the world".
"Look at the size of Bangladesh and Myanmar, compared to us," Abraham Viruthakulangara was quoted as saying.