Rodgers proud of Liverpool youngsters
The Northern Irishman named a youthful side for the trip to Russia, with Conor Coady making his full debut, while 19-year-old full-back Jon Flanagan and 18-year-old striker Adam Morgan also featured.
Former Chelsea winger Joe Cole made just his third start of the campaign after picking up an injury on the opening day of the season, with the midfield also featuring Stewart Downing, Jordan Henderson and Jonjo Shelvey.
"I thought we were outstanding tonight," Rodgers said.
"We were terrific for 44 minutes and 55 seconds in the first half but we just switched off at the crucial moment.
"We created chances throughout and although they got at us a bit more as we pushed on I thought we deserved something out of the game.
"I am very proud of my young players. It was a difficult night but it was a great team performance.
"I thought Conor Coady did very well on his debut and Adam Morgan's movement was good. It is a steep learning curve and when we learn to cut out our mistakes we will be able to go on and win these games."
The Reds now face a tough task if they are to progress to the knockout stages of the competition, although they remain second in Group A behind the Russians.
Swiss side Young Boys surprised Udinese with a 3-2 win at Stadio Friuli to move level on six points with Liverpool and they are the next visitors to Anfield before Rodgers takes his side to Italy in the last group-stage fixture.