Arsene Wenger's side take a 3-0 lead into the second leg of their Champions League play-off tie at the Emirates following an impressive display in Istanbul.
But England international Walcott, who played in Kieran Gibbs for the opening goal in Turkey and was also fouled for the penalty from which Olivier Giroud scored the third, insists they must not consider the tie already won.
"It is nice to take them back to the Emirates (in control of the tie), but we can't be complacent," he said. "We have to be professional, which we will be.
"It is nice to get assists, the next thing will be to get a couple of goals now, but it was more about the team and the performance."
Gibbs also urged caution ahead of the second leg, urging Arsenal to take a positive approach to the game.
"It is still not over because we have got another tie," he said.
"We have to stay focused because you think we are in a strong position, but we now have to think about how we go into the next leg.
"We have to go in on all cylinders again, otherwise if we sit back and think that we are already through it can put us on the back foot, and we don't want that.
"We have to be strong and make sure we finish off the job."