The Gunners led 2-0 at half-time thanks to Mikel Arteta's penalty and Alexis Sanchez's stunning volley before Alex Oxlade-Chamberlain looked to have sealed the win with a third before the hour.
There was late drama, however, as Anthony Vanden Borre scored twice - the second another spot-kick - and Aleksandar Mitrovic headed in a 90th-minute equaliser to snatch a dramatic point for the Belgians.
"Maybe we underestimated them subconsciously and we got punished - in the Champions League you need to be at the right mental level and we got punished because we were not," Wenger said.
"You have to give them credit - they tried until the end.
"We had a poor defensive performance from the first minute to the 90th today.
"We were also punished because of bad luck - the first goal was clearly offside - but defensively our performance was not good enough
We thought the job was done."
Arsenal's misery was compounded by the sight of Arteta hobbling off in the second half with what Wenger revealed is a hamstring injury.
The Gunners remain in a strong position to qualify from Group D but their chances of finishing top of the pool are slim with Dortmund now five points clear.
Wenger's side have gone through second in three out of their last four European campaigns and have lost in the last 16 on each occasion.
"We dropped off too much in the second half and didn't go into the challenges anymore - then you are always open," Wenger continued.
"We stopped winning the challenges and dropped off
We didn't stop the crosses, we didn't stop the long balls.
"In the first half we were outnumbered sometimes but in the second half it was bad defending."
Anderlecht exacted sweet revenge for Arsenal's victory in the reverse fixture a fortnight ago, when the Gunners scored twice in the last three minutes to win 2-1.
The young Belgian outfit were a threat on the break throughout the contest and Wenger admits he was impressed with his opponents.
"Anderlecht are a good team," Wenger said.
"Maybe in four or five years we will see this team was full of good players and they are much better than everyone thinks they are."
"Even in the first half they had three or four good chances - they are a good side."
Anderlecht boss Besnik Hasi believes his players have proved they can cope at the highest level with their two performances against the Gunners.
"We have come from a small competition but we have shown for a second time against Arsenal that we can manage these types of teams and over the two games I think we deserved more than just a point," Hasi said.
"Maybe they thought they wanted to go on and score more goals and have fun with the public.
"I am satisfied with the spirit of my team, I am proud of how they played.
"They are a young team but they showed character today and they showed quality."
There was a hint of fortune around the visitors' first goal as Vanden Borre appeared to be offside when he shot past Wojciech Szczesny.
Hasi, however, was unrepentant.
"I don't know if it was offside and I don't care," Hasi said
"If you saw the last game at home to Arsenal, we didn't get the fouls we should have done.
"I don't think it was lucky."
Source : PA
Source: PA