Nacer Chadli scored in the 56th minute to give Spurs the lead at Emirates Stadium after Mathieu Flamini lost possession of the ball.
But, Oxlade-Chamberlain helped seal a point for Arsenal when he scored from close range in the 74th minute.
Oxlade-Chamberlain told Sky Sports: “We did well to come back, but when we made it 1-1 we pushed on and tried to get the winner.
“Sometimes it’s not about the best football, it’s about who wants to win it more. In the second half we settled down and started to pass the ball more.”
The midfielder scored his first goal of the season yesterday and hopes to score more.
“I'll be working on scoring more as I have the potential to do that, but I also have my role to do defensively,” Oxlade-Chamberlain continued.
“As long as the boss gives me the licence to drive forwards and try and take people on I'm not too fussed where I play.
He added: “We would have liked to have played some better football but it is important that we are not losing games.
“First and foremost we have to defend and then the more fluid side of our game will come.”