The Owls interim manager - in his third temporary stint at Hillsborough, after stepping in when Steve Bruce walked out to join Newcastle United in the summer – enjoyed the perfect start to the campaign with back-to-back wins over Reading and Barnsley.
But despite playing against 10 men for over half the match, Wednesday slipped to a 1-0 defeat at Millwall on Saturday.
Matt Smith’s first-half header – after goalkeeper Keiren Westwood failed to collect Connor Mahoney’s corner – proved decisive.
The Owls bossed possession with their numerical advantage – with 70 per cent of the ball, 21 shots, nine on target – but failed to break down a stubborn defence.
Bullen, whose biggest headache is selecting a match-day 18, having had the luxury of leaving out forward Fernando Forestieri at Millwall, will be hoping the Owls can take out their frustrations tomorrow night when Luton Town arrive at Hillsborough.
A third win of the season, then Saturday’s defeat will be viewed as just a blip.
But, defeat to the promoted Hatters and it will be a big dent in Bullen’s hopes of landing the Owls job a permanent basis.
“It is good that we have a chance to put it right on Tuesday,” said Owls captain Tom Lees. “It will not be an easy game again but it is a chance to put things right.
“We can’t let today affect us too much. If there is a way that you are going to lose, it has got to be how we lost today.
“We have played three teams now so we are not going to get carried away.
“I think you have seen every season that anyone can beat anyone. There are tough fixtures like Millwall that throw up a curve ball so you have got to take each game as it comes.
“We have lost one now so it is important we don’t lose the next one and then, hopefully, it doesn’t seem as bad.
“He (Bullen) knows the league well. We know what we are up against each week and he prepares us for that and we have to go again on Tuesday.
“I’m sure he has a lot of tough decisions now with the strength of the squad and everyone being fit. We have to dust ourselves down and go again on Tuesday.
“It is up to us to go out on the front foot and take the game to the opposition and I am confident we can do that.
“We have to set the tempo ourselves and impose our way of playing on Luton and really put them under some pressure.”
Millwall were reduced to 10 men on 43 minutes, Jed Wallace sent off for a late lunge on Kieran Lee.
But even against a full contingent, the Owls had gone close to opening the scoring with chances for Kadeem Harris and Adam Reach.
After the break, Wednesday chased an equaliser, Bullen’s substitutions hardly subtle – they finished the game with just two recognised defenders on the pitch in Lees and German centre-back Julian Borner – as the visitors pushed men forward.
Jacob Murphy spurned a couple of opportunities, Bartosz Bialkowski thwarted Steve Fletcher and Barry Bannan, and substitute Jordan Rhodes headed wide.
“I thought we controlled the game even with 11,” said Lees. “We moved the ball from side to side and they were just sat inside the box but we couldn’t find a breakthrough.
“If you give a goal away, you have a mountain to climb here (Millwall) because that’s what they love. To be fair to them, they defended their box for their lives.
“We knew it would be a set play if they were going to cause us problems and it ended up being that. I thought we defended the majority of them well but we got caught on one and it gave them something to hold on to.”
Bullen confirmed the decision to leave out Forestieri was tactical, but the forward could return against Luton.
On his future, Bullen added: “All I’m focused on is the next game and that’s all I’ll focus on until the chairman wants to have the conversation.”
Millwall: Bialkowski, Romeo, Pearce, Cooper, Murray Wallace, Mahoney (Leonard 74), Thompson, Williams, Jed Wallace, O’Brien (Ferguson 83), Smith (Bradshaw 52). Unused substitutes: Hutchinson, Steele, Bodvarsson, Skalak.
Sheffield Wednesday: Westwood, Iorfa (Bannan 46), Lees, Borner, Palmer (Luongo 59), Reach, Hutchinson, Lee (Rhodes 65), Murphy, Fletcher, Harris. Unused substitutes: Fox, Nuhiu, Odubajo, Dawson.
Referee: G Ward (Surrey).