Despite a positive display, the young Liverpool stars were unable to find an equaliser in the Stadion Lokomotiv.
Here, Sports Mole takes an in-depth look at the Group A clash.
On target 8
On target 3
Was the result fair?
Over the 90 minutes Liverpool deserved something out of the game. Despite their youth, Rodgers's side controlled the majority of the contest and while the Russian outfit benefited from Traore's strike, they struggled to break down the Reds to take advantage of the inexperience on the field.
The home side started sluggishly in Moscow and while some tipped the Russian outfit to start strong and quick, they were cautious and failed to use their wide players to launch an attacking threat. Guus Hiddink's men improved in the second half and managed to close down their opponents to try to prevent Liverpool from maintaining a rhythm.
The Premier League outfit spread a five-man midfield across the pitch, which proved successful for the Reds in that they were able to spray the ball across the pitch and prevent Anzhi from running riot in the middle of the park. The Reds were let down by individual mistakes and once again they showed that they are struggling to find the net.
Sports Mole's man of the match
Samuel Eto'o: The former Barcelona star was by no means at the level he once was but he was a nuisance to the Liverpool defence when he drifted forward. He had a couple of shots on goal and he provided some well-executed passes to goalscorer Traore but the 31-year-old hampered his performance by dropping deep throughout the first half.
Biggest gaffe of the match
This goes to Liverpool midfielder Jordan Henderson, who wasted the chance to go 1-0 up in the early stages of the match. The former Sunderland player was given a perfectly weighted pass into the penalty area. Henderson timed his run well and was one-on-one with the goalkeeper but he opted for the cross instead of a shot, which handed the ball back to Anzhi.
David Fernandez Borbalan had a positive game in Russia. The Spaniard let the game flow and only administered two yellow cards throughout the contest, which were correctly given.
Anzhi: The Russian outfit welcome Udinese to the Stadion Lokomotiv on November 22 following their league fixture against Rostov.
Liverpool: The Reds go up against Chelsea in the Premier League this Sunday and their next Europa League encounter is against Young Boys at Anfield.