The Reds moved into second in their Champions League group thanks to a double from Oxlade-Chamberlain.
Speaking after the game, he told BT Sport: "I don't know about the Champions League missing me but I've definitely missed it! It was nice to be back out there. It's a special tournament to play in.
"It was great to see the boys do so well last year, being on the bench at the end and watching the boys bring it home.
"It's nice to be back in the starting line-up and to get a couple of goals is a bonus. But we've got to be better if we want to go further in the tournament."