The 18-year-old was somewhat of a surprise inclusion for the Three Lions during the 1-1 draw to France but showed maturity beyond his years in what was only his third appearance for his country.
However, although Oxlade-Chamberlain admits he did not expect to feature against France he insists he does not know if his performance will warrant a start in Kiev for the Group D crunch game against Sweden.
"It's not about me, it's about the team. To come away with the result we did was good"
"There is a lot of competition for places. I'm sure there'll be squad rotation as we've got the players to do it and obviously there are a lot of physical demands from game to game.
"Whether I keep my place isn't for me to say. I'll keep working hard in training and, if I do get the call again, I'll give it my all.
"I was surprised to play against France. But having been picked for the squad in the first place, I had to expect that maybe I'd get the call and had to make sure I was ready.
"It was a big honour for me to represent my country in a major competition."
Although the former Southampton man was not unhappy with his performance, he concedes that the most important factor is the team display and the result which has laid the foundations for England to have a positive tournament.
He continued: "Personally, I think it went okay. I showed in small glimpses and parts what I can do.
"I would have liked to have done a bit better, got on the ball more in different positions where I like to attack players — but it was really hard against a good French side.
"But it's not about me, it's about the team. To come away with the result we did was good. For us to concede only one was good. It was a good point.
"Obviously, we would have liked to win and it was unfortunate that we couldn't hold on to the lead. But the way the game shaped up, they had a lot of possession so a draw was good.
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"We can build from here and definitely get stronger. And we showed our quality as well in glimpses.
"We have got quality in the team — and France also have quality. We'll push on and get stronger from here."
Roy Hodgson's squad now face a 90 minute flight to Kiev where they will take on their next Group D opponents Sweden, and Oxlade-Chamberlain has revealed the players are always kept busy in between matches."We are always kept occupied," he added. "In our off time, we have a lot to do, whether it be table-tennis or pool. It's friendly competition and banter with all the lads.
"The boys have been good, we are not bored or anything. We are thoroughly enjoying the tournament but will enjoy it more if we get results."