"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 on Sunday.
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.
The Algerian statesman briefly served as UN special envoy for Iraq in 2004, following the US-led invasion that toppled the regime of executed dictator Saddam Hussein.
He stressed that he had told the UN Security Council in November that the so-called Islamic State of Iraq and the Levant (ISIL) was "ten times more active in Iraq than in Syria."
This meant Iraq's minority Sunni Arab community was likely to support the extremists, not because they are Takfiri elements but because my enemy's enemy is my friend.
Brahimi added that Iran, a key ally of the government in Baghdad, had "its place" in the region.
Mosul, Iraq’s second city, fell to the hands of the ISIL militants on June 10, before the capture of Tikrit, located 140 kilometers (87 miles) northwest of the capital Baghdad.
Rights groups say around half a million people have been uprooted in and around Mosul.
NTJ/HH