Audrey Cooper's women were brimming with enthusiasm and matched their well-regarded opponents for the majority of the first set.
But a gulf in class eventually appeared, with concentration errors costing Great Britain the opener and giving Russia the platform they needed to secure an opening win 25-19 25-10 25-16.
Russia boast the two tallest players in the tournament and Britain often struggled to find rhythm. But Ciara Michel performed well up high, while Rachel Bragg and Grace Carter also displayed some hitting that will trouble Algeria on Monday.
The British squad took their first point in Olympic competition when Russia touched the net and after that managed to stay toe-to-toe with their opponents through to the first time-out.
Two piercing spikes from Bragg and Lynne Beattie had the audience on their feet, while some impressive work from Michel at the net largely stifled the 6ft 8in Ekaterina Gamova.
Russia found a way to pull clear after that break, edging three points ahead when GB touched the net and then Bragg served long. But Beattie and Carter prevented them from getting too far clear.
However, Bragg committed another service error that saw the gap go to a set-high five points and Russia saw it out 25-19.
Poor serving affected the hosts at the start of the second set too and coach Cooper called a technical time-out to try and steady the ship at 8-3.
The move did not work but to their credit, Britain stayed competitive, with captain Beattie doing her best to rally her team-mates.
However, it was not enough to prevent Russia running away with the match.