"The command of the coalition forces did not use the established communication channel for preventing incidents in Syrian airspace," the defence ministry said in the statement.
Russia said it would now "end co-operation with the American side".
"Any flying objects, including planes and drones of the international coalition, discovered west of the Euphrates River will be tracked as aerial targets by Russia's air defences on and above ground," it said.
The US has been leading the military offensive against Islamic State in Syria and Iraq.
The campaign has often put the US at odds with the regime of Syrian President Bashar al-Assad, which is leading its own attack against IS with air cover support from Russia. Syria is also in the grip of a civil war that has claimed more than 400,000 lives, according to the United Nations.
An American F/A-18 Super Hornet shot down a Syrian SU-22 about 7pm on Sunday. The coalition said the Syrian plane had dropped bombs near its allies, the Syrian Democratic Forces, which were fighting IS south of Tabqah.
Russia said the shooting down of the plane was an act of aggression against Syria and called for a "careful investigation by the US command" into the incident.
"Repeated military actions by US aircraft against the lawful armed forces of a United Nations member state, under the guise of a 'fight against terrorism', are a profound violation of international law and, in fact, military aggression against the Syrian Arab Republic," the Russian Defence Ministry said.
"As a result of the strike, the Syrian plane was destroyed. The Syrian pilot catapulted into an area controlled by Islamic State terrorists. His fate is unknown."
The coalition said the Syrian warplane had been shot down "in accordance with rules of engagement and in collective self-defence of coalition partnered forces".
The deputy chairman of the Russian Senate's defence committee, Frants Klintsevich, said there was "no defence" for the US shooting down the plane.
"Blatant aggression and provocation. To provoke, above all, Russia. It seems that the US under Donald Trump is a source of a qualitatively new level of danger not only in the Middle East but also around the world," he wrote on Facebook.
US authorities are yet to make any formal response to the Russian Defence Ministry statement.
Russia said it would suspend use of the military hotline in April, but it did not follow through on the threat and continued to use the channel.
The April announcement came after US President Donald Trump launched 59 Tomahawk missiles at a Syrian airfield in retaliation for the Syrian government deploying chemical weapons against its own citizens.
The nerve agent attack killed 92 people, including at least 30 children.
