Luol Deng led Great Britain with 26 points and Pops Mensah-Bonsu had 22, but Russia's Andrei Kirilenko was the star of the game with 35 points.
"We knew coming in that Russia are an excellent team," said GB's Rob Archibald after the game. "They execute as well as anyone and they killed us by getting a lot of easy shots.
"We came within 10 points but we just couldn't quite break through and get it into single digits and they pulled away. But that's one out of the way and we know there are more tough games ahead."
GB were impressive early in the game as they built an 11-7 advantage before long-range shooting from Russia saw them snatch the lead and end the quarter 24-19 ahead.
Despite GB twice cutting the deficit to three points early in the second, Russia then took control of the game as they hit GB on the counter, pushing their lead to 38-25.
Mensah-Bonsu made some shots to keep Great Britain within touching distance but Russia took a 49-34 lead into the break.
Both teams came out firing in the third but GB were unable to cut into the deficit and trailed 71-58 going into the final quarter.
Great Britain opened the fourth with a lovely coast-to-coast move from Deng, and his subsequent foul shot made it 66-56. But it was as close as GB would get as Russia claimed the win, pushing the lead to 22 points in the final two minutes.
"We ask Lu to do a lot for us," commented GB Head Coach Chris Finch. "He attacked a lot, I don't know if that was a sign of frustration, but it comes from a good place.
"He is a good attacking player and that's what we will continue to ask of him."
Elsewhere, Team USA began their defence of the gold medal with a comfortable 98-71 win over France. In Great Britain's group, Spain worked hard for a 97-81 win over China, and Brazil edged Australia, 75-71.
GB Men are back in action on Tuesday afternoon (4.45pm tip-off) when they take on Brazil, while on Monday evening the GB Women will look to get their first win when they take on Canada (8pm tip-off).