Mr Miliband said he carried a message of 'real unity'
The foreign secretary has pledged UK support to Georgia during a visit to the country's capital.
David Miliband spoke after talks with Georgian president Mikhail Saakashvili to update him on Nato's reaction.
Mr Miliband said the UK's government and people "stood in solidarity" with the Georgian people.
Russian troops are still in parts of Georgia after a 10-day conflict sparked when Georgia attacked the breakaway region of South Ossetia.
Mr Miliband arrived in Tbilisi following an emergency Nato summit in Brussels.
There, ministers agreed to form a Nato-Georgia commission to help the war-torn state move towards membership of the organisation and to rebuild after August's violence.
Speaking at a news conference, Mr Miliband said he carried a message of "real unity" from the 26 nations of the alliance to Georgia.
"The British policy is founded on very clear foundations, that the rule of force does not replace the rule of law, and the territorial integrity of sovereign nations is to be respected," he said.
"On several counts Russian behaviour over the last 10 days has violated those principles.
"It was striking to hear all Nato members talking about the need to ensure that aggression does not pay."
He also criticised Russia's apparent failure to keep its promises.
"The President of Russia has committed to a ceasefire agreement, including the withdrawal of Russian troops," he said.
"And every day that goes by beyond the deadline of noon yesterday is a day when the world can see that Russia is not living up to its word.
"And that is not just something that is very serious for Georgia. It is very serious for Russia's reputation around the world."
An EU-brokered truce demands Russian forces must withdraw from inside Georgia to their positions before this month's violence.
Conservative leader David Cameron visited Tbilisi last week, saying the West must show solidarity with Georgia.