A fourth defeat was compounded by a serious injury to France right-back Bacary Sagna and Wenger was in a gloomy mood when asked about Arsenal's chances of competing at the top.
"At the moment we have to set ourselves a realistic target to get in touch with those teams who are fighting to stay in the Champions League," Wenger told reporters.
"To say we will win the league is not realistic. We are 12 points behind Manchester United and Manchester City so it is not realistic today to say that we will win the league.
"We have to fight to come back into a much better position."
"The France team doctor, Fabrice Bryand, was informed by his Arsenal colleague of an unstable fracture to Bacary Sagna's right fibula," the FFF statement said.
"No," was his emphatic reply, although with Cesc Fabregas and Samir Nasri gone and Jack Wilshere ruled out until after Christmas with an ankle injury, these are clearly worrying times at Emirates Stadium.
The mood was not improved by the sight of Sagna leaving the ground on crutches although Wenger saw some encouraging signs against Tottenham, who won a fourth consecutive league match with goals from Rafael van der Vaart and Kyle Walker either side of Aaron Ramsey's equaliser.
"In the first half I felt we played a little but with the handbrake on," Wenger said. "Even playing like that we had four chances. At half-time we came out and had a go at them and got it back to 1-1.
"I felt again that we didn't push on enough and let them get back into the game. We lack a little bit of confidence at the moment, and we just need to protect a result when we have one."
Wenger, was rattled by questions over his failure to shake hands with Clive Allen, one of Tottenham's coaching staff, and felt Van der Vaart's opening goal should not have been allowed.
"It is frustrating as well because their first goal was handball," Wenger said. "I wonder what the linesmen do in these situations. It is a second yellow card as well because he already had one - for handball, on purpose."
"They [Arsenal] got off to a better start in the second half, got the goal, and watching the game you would have thought, 'they are in the ascendency. We could be in trouble'," Tottenham manager Harry Redknapp said.
