Six members of the Council, including the United States, the UK and France, rejected the draft resolution in a closed-doors vote on Friday.
"We can only express our regret over the fact that the draft was not supported. Nevertheless, Russia will continue its transparent, consistent and logical course on ensuring stability, fighting terrorism, and protecting territorial integrity of the countries in the region," Peskov said in a conference call with reporters.
A resolution to protect the sovereignty and territory of Syria was proposed by Russia as Turkish forces repeatedly shelled Kurdish-held areas in northern Syria over the past week, claiming they threaten national security and demanding the Kurdish self-defense forces retreat from the northwestern city of Azaz.
Both the United States and Russia have called on Turkey to cease artillery strikes and deescalate tensions. Moscow has repeatedly expressed concern over alleged Turkish plans to carry out a military incursion in Syria.
Earlier in February, the Russian Defense Ministry said that Ankara's activity on the Turkish-Syrian border pointed to intensive preparation for a military incursion in Syria. Later, media reports emerged claiming that Saudi Arabia could deploy ground troops to Syria in likely coordination with Turkey against terrorist groups.
The Kremlin is concerned over growing tensions on the Syria-Turkey border and strongly condemns the shelling of the Syrian territory by Turkey, Dmitry Peskov said.
"The Kremlin is concerned by the growing tension on the Syrian-Turkish border," Peskov said in a conference call with reporters.
"In general, Russia deems it unacceptable that Turkish artillery conducts cross-border shelling of the Syrian territory," Peskov stressed.
On February 13, Turkish artillery began shelling positions held by the Kurdish People's Protection Units (YPG), a Kurdish group with links to the Syrian Kurdish Democratic Union Party (PYD), in Syria's Aleppo Province.