Karlov was killed during an appearance at the Museum of Modern Art in Ankara, the capital. The attack in one of the museum's art galleries was captured on camera.
"He was known for goodness and empathy, features absolutely not associated with the image of bureaucrats as they're normally perceived," Lavrov said in his eulogy, which was broadcast on state TV.
Karlov's coffin was surrounded by an honor guard of Russian soldiers, standing in an ornate marble hall, where most of Russia's senior politicians were present.
Putin did not make a speech, but he did speak afterwards with the wife of the murdered ambassador.
Karlov's coffin was then moved to Moscow's main cathedral, where a service was held.
Karlov, 62, was a career diplomat, according to The Associated Press, who joined the diplomatic service in 1976.
He was Russia's ambassador to North Korea from 2001 to 2006 and later worked as the chief of the Foreign Ministry's consular department. He had been Russia's ambassador to Turkey since 2013.
Turkey's foreign minister said the street where the Russian embassy is located will be re-named after the slain ambassador.
The gunman, Mevlut Mert Altintas, was killed by Turkish antiterror police after the assassination. Altintas was a member of the riot police and had used his police ID card to enter the building before the shooting, according to Interior Ministry sources.
After the shooting, the gunman yelled in Arabic, "Allahu akhbar" (God is great).
He then announced in Turkish, "Don't forget Aleppo. Don't forget Syria. Don't forget Aleppo. Don't forget Syria. Until these places are safe, you will not taste any safety either.”
Police said earlier this week they were investigating many leads and took into custody at least seven people for questioning, including members of Altintas' family.