A 1-1 draw with Manchester United on Sunday, in which the England international opened the scoring before former club-mate Robin van Persie equalised, left the Gunners in fourth in the Premier League, two points ahead of rivals Tottenham Hotspur, who have played a game less.
With Spurs having drawn with Wigan Athletic on Saturday, it was a missed opportunity for Arsenal to open some daylight in the top four and Walcott knows it will be a nervy conclusion to the campaign.
"It is great for you guys," he joked to Sky Sports about the tension after the final whistle against United. "Not so great for us.
"We have just got to concentrate on ourselves. We cannot keep on relying on other teams.
"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)."
But Walcott believes the draw with United will prove to be a point gained come the end of the season.
"I think both teams did not want to lose the game," he said. "In previous weeks, we might have gambled a bit more than we normally do.
"But, overall, come the end of the season, I think it will be a good point."