Diplomats said Annan, a former UN secretary general, was stepping up pressure on the international powers to put some muscle into their support for his peace plan or find a Plan B.
The massacre of more than 100 children, women and men in Houla, the growing threat of all-out civil war and divisions at the UN Security Council -- where Russia has refused to allow any hint of sanctions -- have all highlighted the failure of the international community to pressure President Bashar al-Assad.
"The time is coming, if it is not already here, for a serious review," Annan told Arab League ministers in Doha on Saturday.
"The international community must decide what it does next. From my consultations with many actors, I sense a clear recognition that things cannot continue as they are. I agree," he added.
Calling for greater support for his plan -- under which weapons and troops should be withdrawn from cities and attacks halted so political talks can start -- Annan said: "We must think this through and we must get it right."
Annan will discuss the Syria crisis at the UN Security Council and UN General Assembly on Thursday. Diplomats said Annan's comments were a sign that he can see his peace initiative is failing.
The UN says well over 10,000 people have died in the past 15 months of the uprising and the death toll is speeding up again despite the presence of about 300 unarmed UN military observers.
"He will not admit failure, every word that Kofi Annan says is very measured," said one senior diplomat at the UN. "But as everyone -- from the United States to Russia -- has backed the Annan plan, everyone is noting his comments now and can see the message."
"I think it is clear to everyone now that the international effort to deal with this probably isn't working," said Andrew Tabler, a senior fellow at The Washington Institute for Near East Policy who has worked in Syria.
"Everything has been flipped on its head by Houla and it is not going to get any better. But at least people are now saying that something has to be done sooner rather than later," he added.
Tabler said he could not see any change of course coming from Assad and his entourage.
"They are always fighting for their life. That is just a fact," he said.
The Arab League has called on the Security Council to approve military action to protect civilians.
Permanent council members Russia and China have already vetoed two resolutions that just hinted at sanctions.
Tabler and other analysts and diplomats say that with Russia guarding its major Middle East ally against sanctions, any tough action is now likely to come outside the Security Council. He said the Friends of Syria group, which includes the western powers and key Arab nations, could be a launch pad.
"We have to give the Annan plan a chance, but everyone can see that it is not working so we have to start looking at alternatives," said a second UN diplomat. "The trouble is there is no clear Plan B."
Susan Rice, the US ambassador to the United Nations, said action outside the council may have to be considered because everyone can see the wheels coming off of this bus.
But US Defense Secretary Leon Panetta has insisted that any military action would need UN backing.
Future decisions on Syria will now be made at the Group of 20 summit in Mexico this month and in talks between Western leaders and with Russia's President Vladimir Putin, diplomats said. Putin has however reaffirmed his opposition to sanctions in Paris and Berlin this past week.
The UN observer mission mandate runs out on July 20 but Annan has also indicated that quick decisions are now needed.
"If regional and international divisions play out in Syria, the Syrian people and the region -- your region -- will pay the price," he warned the Arab ministers.