Jihadist-led militants launched a lightning offensive on Monday, advancing to within 80 kilometres of Baghdad's city limits and bringing Iraq's security forces to the brink of collapse.
Brahimi said that the international community's inaction on the conflict in Syria had precipitated the crisis in Iraq.
"It is a well known rule: a conflict of this kind (in Syria) cannot stay confined within the borders of one country," Brahimi told AFP.
The international community "unfortunately neglected the Syrian problem and did not help to resolve it. This is the result," said Brahimi, who resigned from his post as UN-Arab League representative to Syria in May.
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He stressed that he had told the UN Security Council in November that the Islamic State of Iraq and the Levant, the powerful jihadist group spearheading the offensive in Iraq, was "ten times more active in Iraq than in Syria".
"The jihadists' action in Iraq is taking place against a backdrop of a civil war between Shiites and Sunnis," Brahimi said.
This meant Iraq's minority Sunni Arab community was likely to "support the jihadists, not because they are jihadists but because my enemy's enemy is my friend".