The North London club beat the Turks 3-0 in the first leg at the Sukru Saracoglu Stadium on Wednesday night and with the job only half done, Walcott has urged caution ahead of the return bout at the Emirates next week.
"It felt like, with the tempo of game, we dominated it in the centre of park and if we kept on going at a high intensity we'd get a goal, and we did that," he told Sky Sports 1.
"It was three great goals and it's a great result going to the Emirates now on Tuesday night.
"It's nice and comfortable but we've got to be professional on Tuesday. They're going to want to come and make it up to the fans for tonight and we have to be ready for that."