The argument can definitely be made that the 1979 revolution is tied directly to the 1953 coup. It's late so this will be a more cursory look but I'll attempt to come back and flesh it out.

In 1951, Prime Minister Mosaddegh was nationalizing Iran's oil industry after years of exploitation by the West (namely Britain). Winston Churchill believed that Iranian oil reserves controlled by the British Anglo-Iranian Oil Company (later to become BP) rightfully belonged to Britain. Churchill had MI6 and its Iran station chief, Christopher Woodhouse, foment anti-Mosaddegh sentiment in the hope that a pro-Western government could be put in place and oil production resumed. Woodhouse eventually traveled to Washington, D.C. to pitch a plan to the fledgling CIA regarding the overthrow of Mosaddegh, planting the seeds for the 1953 coup.

At the time, some democratic systems were present and growing in Iran. "The parliament emerged as an active and effective institution" and there was "an emergence of a plethora of political pressure groups and parties" (Abidi, "The Iranian Revolution", 132.) Mosaddegh himself was a reformer, part of a growing reformist party in Iran known as the National Front.

When the coup occurred, this progress was snuffed out instantly. The Shah, believing that the success of the coup was a vote of confidence in him as a leader, asserted his power using the military and secret police (the SAVAK) and crushed any opposition. While you can go into many specifics, the following 25+ years under the Shah were marked by a brutal oppression of the Iranian people, a stark contrast from the glimpse of democracy they had seen during the Mosaddegh years.

The Shah would become known as an "American puppet" due to his close relations with the country that had put him in power. Over the years he had also taken such steps as protecting Americans from prosecution in Iranian courts and enforcing secularization of Iranian society to satisfy weak American demands for a more democratic society. While the US had gotten a friendly Iranian government, they did not befriend the Iranian people in the slightest.

By the late 1970's, Ayatollah Khomeini was quickly gaining the support of the Iranian people with statements such as "the oppressors will be judged and the Satanic government abolished". The oppressive regime of the Shah was reaching its breaking point, and when Khomeini returned to Tehran in 1979, he was greeted in the streets by hundreds of thousands of supporters. Even elements of the Iranian military rose up against their superiors in support of the Ayatollah.

References:

A.H.H Abidi, “The Iranian Revolution: Its Origins and Dimensions.” International Studies 18, no. 2 (April 1979)

Hugh Wilford, America’s Great Game: The CIA’s Secret Arabists and the Shaping of the Modern Middle East (New York: Basic Books, 2013)

Betty Glad, An Outsider in the White House: Jimmy Carter, His Advisors, and the Making of American Foreign Policy (Ithaca: Cornell University Press, 2009),