The Gunners remained fourth after today's 1-1 draw with champions Manchester United at the Emirates Stadium with Walcott scoring an early opener before ex-skipper Robin van Persie levelled from the penalty spot.
The draw left Arsenal two points ahead of North London rivals Tottenham, who have a game in hand, and Walcott said it was all up to the Gunners to secure wins in each of their last three fixtures to ensure Champions League football for next season.
"We have just got to concentrate on ourselves. We cannot keep on relying on other teams," he told Sky Sports.
"As long as we get the three points and do not drop any points, that is all we can do.
"Hopefully, come the end of the season, we have kept that undefeated run of games. We need to make sure we are definitely there (in the top four)."