A point at Blackburn on Monday would have effectively secured their position as they have a superior goal difference but they lost 2-1 at Ewood Park.
Should Spurs win their remaining two matches - against Manchester City and Burnley - and the Gunners lose at home to Fulham on Sunday Arsenal would suffer the ignominy of finishing below their north London neighbours.
However, Wenger has dismissed such a scenario.
"I believe we do not have to worry about Tottenham or Manchester City - we have to worry about us and finish the season well," said the Frenchman, whose side have lost at the Emirates Stadium just twice this season.
What Wenger has to be wary of though is his players' increasing lack of desire, which was evident in the performance against Blackburn.
Having taken an early lead through Robin van Persie they were not prepared to battle it out with Rovers and when the home side turned the score around it was fully deserved.
Wenger acknowledged what the problem was in his team's seventh away defeat of the season - they have lost the last two away and not won in four on the road - but is hopeful it will not manifest itself at home on the final day of the campaign.
"There were some individual performances which would explain that, the fact Blackburn defended well and they were sharper in the fight than us - in the one-against-one they were better than us," added the Frenchman, who revealed he was "completely disinterested" in the championship battle between Chelsea and Manchester United.
"Overall Blackburn were sharper in the duels and in the fight than us and then it becomes very difficult to win football games.
"Because we are not in the [title] race any more of course something has gone in the belief.
"That is why we have lost the last two away games. But there is one game to go and we don't play away we play at home."
Arsenal defender William Gallas, who has missed the last month of the season through injury, has confirmed he expects to be fit for the World Cup.
The France international, who is out of contract at the end of the campaign, expects to have fully recovered from a calf problem to feature in Raymond Domenech's squad.
"I will be ready for France," Gallas told Le Parisien.
"Had it not been possible [to recover] I would have pulled out but right now I feel good and ready for France."