Oxlade-Chamberlain earned his first league start under Jurgen Klopp at the London Stadium and scored the third in Liverpool's resounding 4-1 win, his effort adding to Mohamed Salah's brace and Joel Matip's tap-in.
It came at a crucial juncture for the visitors, who had seen Manuel Lanzini halve the deficit less than 60 seconds earlier, and Oxlade-Chamberlain felt Saturday's success was a hugely positive step both for him and the team.
"It wasn't an easy game, it was an intense game. It was crucial we responded well [to Lanzini's goal] and from then on out we defended well," Oxlade-Chamberlain told BT Sport .
"We know on the counter we're a big threat, we created a lot of chances and we could have had more.
"It takes time to settle in and learn a new style. I feel like I'm getting there and it's always important to show what I can do and that's scoring goals and helping the team to win.
"I need to keep improving, there's a lot more to come from me.
"We've got to focus on ourselves, there are some big games tomorrow but we needed to win today, especially before the [international] break and we did that today so I'm really happy."