Wednesday were within touching distance of a third successive win under his control but for a 95th minute own goal.
"It was devastating at the end. You walk in after that and it feels like a defeat," Bullen said.
"I am sure that Darren feels like it is a victory. But I thought that we had done enough.
"It is very frustrating but the players deserve a lot of credit.
"The disappointing thing is when they went down to 10 men, we didn't show enough composure on the ball. We kept handing the ball back to them.
"When I came in, I concentrated on getting the team more compact and tight. It's worked a treat until the goal."
Meanwhile, Bullen remains in the dark over how long he will remain in caretaker charge with Steve Bruce widely expected to take charge at Hillsborough in the near future.
"The job will take care of itself," he added. "I know nothing more. It's in the hands of the chairman. I'll just plan towards Birmingham (their next game) until anything changes.
"It's not a frustration for me, I'm living the dream at the moment. My history and love for the club is well known.
"I don't see this as frustrating in any way. I've not been told Steve Bruce has the job.
"I read the media like everyone but I've not been told anything.
"I'm just loving it. If the chairman wants to tell me something, he'll tell me something. He's told me to take the team and I'm really enjoying it."
West Brom manager Darren Moore praised the resilience of his side after their late heroics rescued a point in a 1-1 Sky Bet Championship draw against Sheffield Wednesday at the Hawthorns.
Albion were trailing to Atdhe Nuhiu's fifth-minute strike and were reduced to 10 men in the 63rd minute when striker Jay Rodriguez was sent off for an alleged stamp on Marco Matias - a decision that Moore plans to appeal.
But skipper Chris Brunt earned Albion a vital point in stoppage-time as they extended their unbeaten run to nine games.
"I am sitting here and I am absolutely delighted with the point with it coming so late," Moore said.
"The reasons for that are it being the second game in three days, playing the last half-an-hour with 10 men, the attitude of the players, the relentless approach to get back into the game; the stadium still being full in the dying moments and that showed real togetherness from the whole football club and that is something we have been working hard at getting back here.
"I am sharing with you exactly what I said to the players. It is as good a point won that I have ever felt in terms of the magnitude of the game."
Moore hopes to get Rodriguez's red card overturned as he faces a three-match ban if it stands.
"Initially when I saw the red card go up I was so surprised as Jay is an honest hard-working individual," he added.
"When he came off he said: 'gaffer, I didn't touch him'.
"I believe that. It looked a nothing incident. I would like to appeal it as it is a straight red and a three-game ban."