Nasrallah's remarks were Hezbollah's first response to the border skirmish.
He said Hezbollah's fighters were ordered not to get involved, but that they had been put "at the disposal of the army" after the clashes started.
"We called the president, the speaker of the parliament, the prime minister, and we said, we will not take any action, despite the great pain we feel," Nasrallah said.
He praised the Lebanese army for its "absolute bravery" during the attack.
The Hezbollah leader also once again addressed the Special Tribunal for Lebanon, the UN-backed panel investigating the 2006 assassination of Rafiq al-Hariri, the former prime minister.
Taking an defiant tone, Nasrallah accused Israel of murdering al-Hariri, and promised to unveil proof during a news conference scheduled for next Monday.
He also accused Israel of manipulating the tribunal to create sectarian tensions in Lebanon.
"The Israeli media spoke happily about how Hezbollah would be indicted, about how it would cause the Lebanese to fight each other," Nasrallah said.
Nasrallah revealed last month that the tribunal would indict several members of Hezbollah.
But he called them "rogue elements," and said that Saad al-Hariri, the Lebanese prime minister and Rafiq al-Hariri's son, assured him he would publicly avow that they were "undisciplined members" of the group.