At the same time, Washington and allies must press Syrian rebels to negotiate with people linked to the regime, Annan said in an opinion article published by The Financial Times, the day after he announced his resignation from the diplomatic role that he said some called "Mission: Impossible."
"Military means alone will not end the crisis," Annan wrote of the upheaval that began 17 months ago as a peaceful uprising against Assad and is now a civil war.
"There are clear common interests among the regional and international powers in a managed political transition," he wrote, calling on "all countries with influence over the actors on the ground ... to press upon the parties that a political solution is essential.
"For Russia, China and Iran this means they must take concerted efforts to persuade Syria's leadership to change course and embrace a political transition, realizing the current government has lost all legitimacy," Annan said in the article headlined, "My Departing Advice on How to Save Syria."
The Syrian regime -- which Annan described as "40 years of dictatorship" -- must make the first move, Annan wrote.
"Its intransigence and refusal to implement the six-point peace plan has been the greatest obstacle to any peaceful political process, ensuring the distrust of the opposition in proposals for a negotiated transition," he wrote.
"For the U.S., U.K., France, Turkey, Saudi Arabia and Qatar this means pressing the opposition to embrace a fully inclusive political process -- that will include communities and institutions currently associated with the [Syrian] government," he wrote. "This also means recognizing that the future of Syria rises and falls on more than the fate of just one man.
"It is clear that President Bashar Assad must leave office," Annan said. "The greater focus, however, must be on measures and structures to secure a peaceful long-term transition to avoid a chaotic collapse."
Annan was critical in his piece -- and in a news conference at U.N. offices in Geneva, Switzerland, announcing his departure -- of what he called "finger-pointing and name-calling in the Security Council," which he said stymied his efforts.
U.N. Secretary-General Ban Ki-moon said in a statement a search was on for a successor to Annan, who will serve until the end of this month, when his mandate expires.
"Let me say that the world is full of crazy people like me, so don't be surprised if someone else decides to take it on," Annan, 74, a Nobel Peace laureate and former U.N. secretary-general, told reporters.
It was unclear what his resignation meant for the U.N. Syrian observer mission the Security Council created as part of Annan's peace plan. The mission suspended most work in mid-June because of the violence and its mandate is to expire Aug. 19.
White House spokesman Jay Carney called Annan's resignation "very unfortunate" and said it highlighted "the failure at the United Nations Security Council of Russia and China to support resolutions -- meaningful resolutions -- against Assad that would have held Assad accountable for his failure to abide by his commitments under the Annan plan."
Russian President Vladimir Putin called Annan a "very respectable person, a brilliant diplomat and a very decent man, so it's really a shame," the non-governmental Russian news agency Interfax reported.
The official Syrian Arab News Agency said on Facebook, "Syria regrets [the] resignation of Annan, stresses [its] commitment to cooperating with [the] observers."
No immediate comment was attributed to Assad or to the various Syrian opposition groups, some of which had expressed doubts about Annan's efforts.
The U.N. General Assembly was to vote Friday on a non-binding resolution drafted by Saudi Arabia demanding Syrian compliance with Annan's peace plan.
Russian U.N. Ambassador Vitaly Churkin said Thursday Moscow opposed the resolution, calling it unfairly biased against the Assad regime.