The North London club are two points off the relegation zone and battling with injuries, and Wenger says fans should now hope for a top-four finish instead of silverware.
"We are 12 points behind Manchester United and Manchester City, so it's not realistic to say that we will win the league," Wenger said in an email to supporters.
"We have to fight to come back into a much better position, that's the reality."
"Obviously we are not where we want to be in the Premier League table and I think at the moment we have to set ourselves a realistic target and stay in touch with the teams who are fighting for the Champions League positions."
Defeat to Spurs on the weekend has left Arsenal at 15th in the Premier League table with four losses.