The win meant Arsene Wenger's men moved to the top of the table, a point ahead of Leicester City, who host fourth-placed Manchester City on Tuesday.
"We're in a strong position now, it's where we would like to be," Oxlade-Chamberlain told the club's website (www.arsenal.com).
"There have been some hiccups along the way and I'm sure there will be a few more but we need to build on this half of the season and go into the New Year positively and in the right manner.
"You need to build momentum. It's all about getting the right results and as many results as possible from here.
"From day to day, we need to turn it around if we have a bad result. We need to turn that around and we got the right result."
"We know we're capable of winning games. The boss said to us that the team that lost at Southampton is no different to the one that beat Manchester City at home."
With Alexis Sanchez, Santi Cazorla, Francis Coquelin, Mikel Arteta, Jack Wilshere, Tomas Rosicky and Danny Welbeck all ruled out with injury, Oxlade-Chamberlain hoped for a quick recovery for his team mates.
"We'll hopefully get some injured players back soon and that will boost us again, but the boys have been really good so far," Oxlade-Chamberlain said.
"We need to keep that going and today was a good step and a good way to end the year."
(Reporting by Shravanth Vijayakumar in Bengaluru; editing by Sudipto Ganguly)
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