Russia accused Ukrainian police of doing nothing to stop the attack, and called it a "grave violation of Ukraine's international obligations".
Meanwhile NATO released images which it says back up Ukrainian claims that Russian tanks crossed into Ukraine.
Moscow has denied sending the tanks to help pro-Russian rebels in the east.
A range of images show the T-64 tanks first at a Russian military staging area near Rostov-on-Don, and then apparently inside Ukraine earlier this week.
Unlike Ukrainian armoured vehicles, the tanks have no markings or camouflage.
NATO says the pictures "raise significant questions'' about Russia's role in eastern Ukraine.
Now NATO has released satellite imagery, linked to existing video material, which appears to give added weight to assertions from the Ukrainian authorities that the tanks used by separatist forces that crossed into its country just a few days ago were indeed supplied by the Russians.
The evidence shown comes from NATO military sources and is not necessarily conclusive.
But, despite Russian denials, it is strongly suggestive of the narrative that NATO is setting out.
It should be noted that Russian spokesmen have denied a number of things in regard to operations in Ukraine which have turned out to be untrue.
Saturday's disturbance in Kiev occurred when several hundred protesters hurled eggs and paint at the Russian embassy.
One petrol bomb was also hurled, windows smashed and a flag torn down.
The protesters - some wearing balaclavas - overturned cars with diplomatic plates.
One protester held a sign saying: "Russia is a killer."
Russia's protest against the incident was echoed by the US state department.
"The United States condemns the attack on the Russian embassy in Kiev, and calls on Ukrainian authorities to meet their Vienna convention obligations to provide adequate security," it said.
Earlier on Saturday, Ukrainian President Petro Poroshenko vowed to retaliate against pro-Russia separatists in the east after a military plane was shot down by anti-aircraft fire, killing all 49 people on board.
Those involved in such "cynical acts of terrorism" must be punished, said Mr Poroshenko, who summoned security officials for an emergency meeting.
The Ilyushin-76 transport was attacked by separatist forces as it was about to land in the city of Luhansk.
Pro-Russian fighters have been searching the site for usable ammunition, as David Stern reports.
It is thought to be the biggest loss of life suffered by government forces in a single incident since the Ukrainian government in Kiev began an operation to try to defeat the insurgency in the east.
Rebel fighters were seen combing through the charred wreckage of the plane, south-east of Luhansk, on Saturday.
"This is how we work," one of them, who identified himself as Pyotr, told Reuters news agency.
"The fascists can bring as many reinforcements as they want but we will do this every time."
The incident came less than a week after pro-Russia rebels launched a series of attacks on Ukrainian forces at Luhansk International Airport.
The airport has been under the control of government forces but the rebels hold most of the rest of the city.
The eastern regions of Donetsk and Luhansk declared independence last month.
In March Russia annexed the Crimean peninsula in the wake of the removal of Ukraine's pro-Moscow President Viktor Yanukovych.
The "anti-terrorist operation" by Ukrainian government forces has left at least 270 people dead over the past two months.
Mr Poroshenko had said that fighting must end "this week" following his inauguration last Sunday.
Source: BBC News Europe