The Kremlin said Putin also warned Netanyahu against carrying out such operations in the future.
Putin “reminded” Netanyahu that such operations “violated Syrian sovereignty” and said “agreements around the prevention of dangerous incidents were not observed”.
“The president of Russia urged the Israeli side not to allow such situations from now on,” it added.
The plane, downed by Syria’s Russian-made S-200 air defence system, had a crew of 15 who were all killed, Moscow said.
The Russian military accused Israeli pilots of using “the Russian plane as a cover, exposing it to fire from Syrian air defences”.
Israel denied the accusations, saying its jets were already back in Israeli airspace when Syrian forces launched the missiles that hit the Russian plane.
Russia stressed the incident would have no impact on the Idlib deal, but warned Israel of reprisals and summoned its envoy in Moscow.
US Secretary of State Mike Pompeo also expressed “sorrow” over the Russian deaths, and said the incident showed “the danger of tragic miscalculation in Syria’s crowded theatre of operations”.
The Syrian Observatory for Human Rights said some missiles, suspected to be Israeli, did get through the Syrian defences and struck ammunition depots at the site of the technical industries institute.
Rami Abdel Rahman, the head of the Britain-based monitoring group, said at least two fighters were killed and 10 wounded in the strike.
Israel has conducted frequent raids in recent months against Syria’s military infrastructure, including against bases it believes host Iranian combatants.
Earlier in September, Israel admitted carrying out 200 strikes in Syria over the past 18 months.