The Abu Dhabi club's head coach watched in frustration as his team failed to break down their struggling opponents, who played the last 27 minutes with only 10 men.
The Wahda fans could even be heard voicing their anger outside the stadium as Hickersberger spoke at the post-match news conference.
"Our fans are right to be angry because they expected us to win this game and we couldn't deliver," he said. "They are angry at me, of course, and that is OK. I am old enough to acknowledge this and it's not a problem for me.
"We did not underestimate our opponents. The players knew in advance that it would be difficult. I am very disappointed. We have to admit that we did not do our job properly."
Dubai remain at the foot of the Pro League with two points from five games after this draw.
Ion Marin, their Romanian head coach, was delighted with the way his players rose to this challenge.
"To take a point from Al Wahda is a very good result for is," he said. "This is an excellent result and I have to say the players did really well. It is true that our defence was put under some strain in the second half, but we managed to keep them out. We could even have won the game but a draw was right.
"I think we can get better and when all of our injured players come back we will start to win football matches."
Wahda had been beaten 2-1 away by Dubai in the Etisalat Cup and the home side found out after only 11 minutes that this was going to be another testing encounter.
A 30-yard free kick from Simon Feindouno, Dubai's Guinean forward, was tamely palmed away by Mutaz Abdulla, the goalkeeper, into the path of Abou Baca Camara, who had the presence of mind to centre the ball, rather than shoot, and Jasim Mubarak was given the simple task of tapping home from close range.
Wahda huffed and puffed for a good while and grew frustrated as shots were blocked and last ditch challenges thwarted their efforts.
However, it came good for the home team on 29 minutes when Fernando Baiano, the Brazilian striker, controlled a pass on his chest and volleyed past Jamal Abdallah Ali, the Dubai keeper, to equalise. But that marked the end of the scoring.
Dubai went down to 10 men on 63 minutes when Ismaeil Ahmed picked up a second booking for a trip on Ibraheem Alawi, the Wahda substitute.
That should have set it up for hosts, but it was only in the final five minutes of added time that Wahda bombarded their opponents' box with cross balls, but to no avail.
Indeed, in the last minute Dubai's Hassan Mohamed was through on goal and should have scored an unlikely winner, but his chip was inaccurate and trickled harmlessly wide.
It got worse for Wahda after the final whistle.
"Basheer Saeed was given two yellow cards by the referee after the game because he was complaining about Dubai's time wasting," said Hickersberger. "He is an experienced player but even he got frustrated."