In addition to Netanyahu, Modi also met Israeli President Reuven Rivlin on Wednesday.
Modi met Abbas in New Delhi in May.
"We expected him [Modi] to visit both Israel and Palestine," Palestinian Deputy Foreign Minister Tasir Jaradat told Al Jazeera.
"To play an important role between the two sides and to be able to spread the message of peace, one should visit both."
India, which has a history of advocating the Palestinian cause, opened up formal diplomatic ties with Israel in 1992.
During the Cold War, India was a leading member of the Non-Aligned Movement of developing countries and sided staunchly with the Palestinians in their conflict with Israel.
Before 1992, India would not even allow its citizens to enter Israel on an Indian passport.
But since then, the two countries have cultivated warm ties, particularly in the areas of technology and defence cooperation.
It is common for world leaders to also travel to Ramallah in the occupied West Bank during official trips to Israel.
US President Donald Trump held talks with Netanyahu and Abbas on his visit in May.
The snub by Modi also attracted criticism from residents of the Gaza Strip and occupied West Bank.
"It's very sad that Modi did not come to Palestine," Ali Mohammad Abushbak, a Palestinian student, told The Indian Express.
"A lot of people believe the story of Israel, but what about the Palestine story? We are feeling discriminated [against] by this approach of the Indian government."
India is seeking closer defence ties with Israel, particularly as it moves away from relying on traditional ally Russia for its military hardware.
Al Jazeera's Harry Fawcett, reporting from Jerusalem, said: "The PA is talking in terms of surprise, rather than outright criticism, that Narendra Modi has decided not to make time for its president in the course of a three-day visit."
Source: Al Jazeera and news agencies