Saturday's crash occurred after at least eight Israeli fighter jets launched a retaliatory airstrike against the airfield suspected to have launched the drone.
"We urge all the involved parties to exercise restraint and avoid any steps that could lead to the aggravation of the situation".
He did not say whether the drone was armed or for reconnaissance, but alleged it "was on a military mission sent by Iranian military forces" from an "Iranian base" in the Palmyra area.
The Israeli action came following the IDF's announcement that one of its military jets had crashed after coming under fire from anti-aircraft missiles in Syria.
The Israeli military confirmed that the F-16 had gone down in Palestine's northern occupied territories, and that the two pilots had been transferred to hospital after ejecting out safely.
Tensions have also spiked across the frontier between Israel and Lebanon over Israeli plans for border wall, and Lebanese plans to exploit an offshore energy block which is partly located in disputed waters.
A State Department official said the Trump administration is "deeply concerned" by an escalation of military action along Israel's northern border with Syria, and "strongly supports Israel's sovereign right to defend itself".
Israel has issued several warnings about the presence of Iranian forces in Syria.
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"This is the most blatant and severe Iranian violation of Israeli sovereignty in the last years", Conricus told journalists in a phone conference.
Netanyahu accused Iran of violating Israel's sovereignty by dispatching a drone from Syrian territory into Israel on Saturday morning. "It is absolutely unacceptable to create threats to the lives and security of Russian servicemen who are in Syria at the invitation of its legitimate government to assist in the fight against terrorists", the ministry said.
The statement also warned Israel that it will respond "crushingly and seriously".
Conricus, IDF spokesman, maintains Iran is the aggressor and Israel's military is "ready for all scenarios".
The Syrian conflict is maybe reaching its end game and Israel has made its red lines very clear.
"This is a dramatic development", Al Jazeera's Zeina Khodr, reporting from Lebanon's capital, Beirut, said.
Lebanon protested Israel's use of its airspace to target Syria, saying it will complain to the United Nations Security Council.
"I emphasized in the talk with him [Putin] that it is our [Israeli] right and duty to defend themselves from attacks from Syria", Netanyahu said.
"Reports of downing an Iranian drone flying over Israel and also Iran's involvement in attacking an Israeli jet are so ridiculous..."