The Gunners ran out 2-0 winners at the Stadium of Light after some sloppy defending allowed Alexis Sanchez to notch an easy double.
Oxlade-Chamberlain is not concerned about the nature of the win, however, only that the Gunners were able to turn their recent draws into a win.
"It's been a little problem of late, drawing too many games that we should have won, so we knew it was really important for us to coming here today," the 21-year-old told Sky Sports News.
"It's always hard playing at Sunderland, on the back of their last result we knew that they'd be keen to prove themselves this week, we knew they'd come out of the traps and we had to match them and as the game went on find a few openings to punish them, and we did that.
"I think we'll say that we deserved the win, I think we dominated a lot of the ball. In the second half they came out better than they did in the first. We didn't pass the ball as well as we we would have liked in the second half, but then it's always important that we can grind out results, and we've done that today."