Jeffrey Feltman, speaking after briefing the Security Council, said that the solution must be through a Syrian-led political process and "must bring real change and a clean break from the past."
Britain's UN Ambassador Mark Lyall Grant said Mr Brahimi is hoping "that everyone will be more pro-active," but he said the onus is especially on Russia and China which have vetoed three UN resolutions on Syria.
He spoke after another bloody day in Damascus where gunmen killed the brother of Syria's parliament speaker.
Mohammed Osama Laham, the brother of Parliament Speaker Jihad Laham, became the latest victim of a wave of assassinations targeting Syrian officials, army officers and other prominent supporters of President Bashar Assad's regime.
Four of the leader's top security officials were killed in a rebel bombing on the state security headquarters in July.
Mr Laham was gunned down in the Damascus neighbourhood of Midan, the SANA state news agency said. The killing came a day after some of the most intense fighting in Damascus in months as rebels wage a civil war to unseat Assad.
The government and activists said a series of explosions rocked the north-western edge of Damascus. At least 15 people were killed and 30 wounded, according to a government official. SANA said three blasts occurred in the al-Wuroud district near the town of Qudsaya, causing significant destruction.
Activists said the bombs were placed in a main square near housing for the country's elite troops.
Mr Brahimi, who, like his predecessor Kofi Annan has been unable to put an end to the 19-month-old civil war, called the events in Syria a "big catastrophe."
In remarks in the pan-Arab daily 'Al Hayat', he said international efforts now are focused on getting a "binding resolution by the (UN) Security Council" to start a political process that will lead to change.
"I don't want to go too far in pessimism, but the situation in Syria is very dangerous. The Syrian people are suffering a lot," Mr Brahimi said. "I believe that if the crisis is not solved in a right way, there will be the danger of Somalisation. It will mean the fall of the state, rise of war lords and militias."
The east African nation of Somalia has been mired in conflict for two decades after warlords overthrew a dictator in 1991 and then turned on each other. The government, backed by African Union troops, is currently battling Islamist extremist rebels linked to al-Qa'ida.
The Syrian conflict's already increasing sectarian overtones suggest any power vacuum could usher in a direct fight among the communities.
Dozens of opposition groups and rebel brigades have taken up the fight against Assad, but they share little common vision for the future and are divided by acute ideological differences, particularly among secularists and Islamists.
Diplomacy has failed miserably in ending the conflict in Syria, which activists say has killed more than 36,000 people.
British Prime Minister David Cameron suggested yesterday that Assad could be allowed safe passage out of the country if that option would guarantee an end to the nation's civil war.
Asked in an interview if he would contemplate offering Assad an exit route, Mr Cameron said the international community would consider anything "to have a safe transition in Syria."
Officials said Mr Cameron was not suggesting Assad could escape potential international prosecution.