Former Gunner Jeremie Aliadiere denied Wenger's side victory with a glancing header past Manuel Almunia in the 35th minute, canceling out Emmanuel Adebayor's early opener.
Despite falling behind in the Championship race Wenger said: "We believe that champions are people who go on when everybody else stops.
"That's the way we can show it. Nobody believes in us but we can show we still believe and keep going.
"I believe at the moment my team needs encouragement more than anything."
The Frenchman added: "I must say I expected them (Boro) to collapse a bit more than they did in the final part of the game and they didn't give in.
"They kept going even when they had tired legs and that's credit to them."