Oxlade-Chamberlain capped off the rout at Anfield with a well-taken fifth goal after earlier strikes from Philippe Coutinho, Roberto Firmino (2) and Trent Alexander-Arnold had put Liverpool in control.
However, the England international was not pleased with his display despite the convincing victory and has set his sights on improving in the future.
"I was a bit disappointed with myself today, although I'm happy to score. When the chance came at the end I was happy to put it away," Oxlade-Chamberlain told Sky Sports News.
"In the first half we did OK and we stepped it up in the second half. I just want more out of myself. I could have done better with my end product a few times. Overall it could have been better.
"I just want to keep pushing myself on to do better. It's important for me [to score]. Today [the goal] wasn't so crucial as we were leading by a few but I need to keep doing that. There were some great goals today. We defended well overall."
The victory lifted Liverpool back up to fourth in the Premier League table ahead of Saturday's meeting with Leicester City.