Chances were few and far between for both teams as Bruce extended his unbeaten run since taking charge of the Owls at the start of February and is yet to see his defence concede a goal.
Bruce looks to have shored things up at the back but wants to see more threat going forward if he is to lift Wednesday further away from the relegation zone.
"Both teams had a colour clash with the strips and forgot how to pass it to each other," said Bruce. "It was always going to be difficult, I never expect anything other than difficulty when you come here.
"The one thing you have to be is prepared and be brave to take the ball. I thought we were better second half when we made the switch we might have nicked it at the death.
"We had to be solid and the keeper has played very, very well. He's given us a calmness. The thing we wanted to arrest when we came in was to stop conceding two every game.
"The back four and the goalkeeper, since I've walked through the door, have done tremendously well with the help of the other players around them.
"We need to show a bit more in the final third. We lacked that bit of quality and that's one thing we'll have to improve."
Neil Harris has been at Millwall for almost 20 years and believes that the direct football they played when he first arrived is still the best means of getting results going forwards.
Few people know Millwall as well as Harris, and the Lions boss was pleased with his team's defensive performance but remains adamant he has quality players that should be doing the job in front of goal.
"There's been an element of people saying we're too direct. Well direct has been good for us, ever since I joined the football club in 1999. It's been very effective. We're very difficult to play against," said Harris.
"I focus on the positives. First half was outstanding, we dominated the game. Jordan (Archer) kicked the ball once in 27 minutes.
"That's how much we dominated possession and we got in some really good areas in behind their full-backs and around the penalty area.
"Around the area we have to do better, I've got quality players and expect better end product.
"The good thing for me is we're back to being very hard to beat, especially here. If you can't win the game, you want to keep a clean sheet and get a point.
"That was important tonight, another solid defensive display."