The November 19 bomb attacks on the Iranian embassy came amid major regime offensives on several key fronts in Syria's brutal war, among them Damascus province and Aleppo.
A day after the attack, Saudi Arabia condemned the "cowardly and terrorist" bombings.
In his remarks to OTV, Nasrallah said the blasts that hit the embassy, which is located in Hezbollah's southern Beirut bastion, were "linked to Saudi Arabia's rage against Iran over its failure" in Syria.
Saudi Arabia is "making Iran pay the price for the consequences of the failure of its plans in the region," he added.
While Riyadh's regional rival Tehran has "tried for years to open the doors (for talks) with Saudi Arabia, the one that closed all the doors and windows... was Saudi Arabia," said Nasrallah.
"The problem with Saudi Arabia since the beginning is that it has dealt with Iran as an enemy," he added.
"Saudi Arabia seeks to impose itself as the leader of the Arab and Muslim world, and refuses any friend or companion. It wants all the governments of the Arab and Muslim world to follow (its) orders."
Nasrallah meanwhile said Iran's nuclear deal with the Western so-called P5+1 powers has "delayed war for the long run," even as it remains a "temporary" accord.
Under an interim deal signed on November 24 with the United States, France, Britain, China and Germany, Iran agreed to limit uranium enrichment in exchange for minor relief from UN and Western sanctions.
The Saudi government reacted cautiously to the deal, saying the deal could mark the first step towards a comprehensive solution for Iran's nuclear programme, "if there are good intentions."
Hezbollah fighting in Syria 'to protect Lebanon'
On Hezbollah's controversial involvement in Syria's brutal war, which in 32 months has left more than 126,000 dead and forced millions more to flee their homes, Nasrallah said his movement has sent in fighters "to protect Lebanon."
"Should Syria fall into the hands of these (rebel) armed groups, what will Lebanon's future be?" Nasrallah asked.
"We went to Syria to defend all of Lebanon."
He also said "most car bombs that were sent to Lebanon came from Yabrud and Nabuk" in Damascus province, where Syria's army and pro-Assad militia are fighting to crush rebel positions.
Hezbollah's stronghold in the southern suburbs of Beirut was hit by two car bomb attacks this summer, one of which killed 27 people.
Attacks in the northern city of Tripoli, the majority of whose residents are Sunni and support the anti-Assad revolt in neighbouring Syria, in late August killed 45 people.
While Hezbollah's involvement in the Syria war has stoked much criticism from the opposition, he said "there were come a day when all those... will thank us."
Nasrallah also said Hezbollah's intervention in Syria was "gradual," and that its fighters are now engaged in fighting around Damascus, near the Lebanese border and in the central province of Homs.
Hezbollah first admitted sending fighters into Syria in May this year, when it fought alongside regime troops to take back Qusayr, a key former rebel stronghold in Homs province near Lebanon's border.
Ever since, it has sent thousands of fighters into Syria to back Assad's troops, in a decision which Nasrallah said the group took independently, rather than under Tehran's directives.
"We did not enter Syria under an Iranian decision. This was our decision, and we informed our brothers in Iran of it," said the Hezbollah chief.
By intervening in Syria's war, "we mitigated the losses and repercussions of the situation in Syria on Lebanon," he added.
Lebanon is sharply divided over Syria's war, though the state's official stance on the conflict is of neutrality.
Frequent Syria-related fighting has broken out in Lebanon, particularly in Tripoli, which on Monday was placed under the Lebanese army's control for six months after the latest round of sectarian fighting killed 11 people.
Syria dominated Lebanon militarily and politically for 30 years until 2005.