Murphy was one of three goalkeepers name in Giovanni Trapattoni's squad for the European Championship qualifier, but Manchester City's Shay Given played the full game with Coventry City's Keiran Westwood on the bench.
The visitors took a 3-0 lead, with late goals from Robbie Keane and Shane Long not enough to earn the Republic a point.
"Over 90 minutes Russia deserved to win," said Trapattoni, who thought Russia would take up a more defensive approach.
"I didn't think we would concede three goals, but we showed character because we could have conceded more."
Murphy will stay with the Republic squad as they head to the Slovakian capital of Bratislava for another qualifier on Tuesday night.