Liam Lindsay was sent off after half an hour after a bright start from the Lilywhites on the road, notably in a 4-3-3 formation for the first time under manager Ryan Lowe.
Derby were also reduced to 10 after Max Bird was giving his marching orders 10 minutes into the second half but the Rams went on to score the only goal of the game.
Ravel Morrison volleyed past Daniel Iversen despite two excellent saves from the Dane, as North End failed to deal with a corner.
Bauer told the Lancashire Post: "It was a disappointing result, we worked all week on the system and it's just disappointing to come here and lose.
"We wanted to get a good results and that unfortunately didn't happen.
"It was frustrating when we got the sending off because having worked on the system all week we then had to switch to back three.
"But things like that happen, I think we could have cleared the ball earlier and then he wouldn't have been in that situation.
"Even with the sending off I felt that we could win the game, unfortunately we conceded from a set play in the second half.
"We moved to the back three and we're really used to that system so I felt we could still go on and win it - my feeling was that if we keep a clean sheet here, we win the game.
"We haven't played much in a 4-3-3 but we had everything set, it was frustrating that we couldn't get the win today.
"We didn't create a lot of chances and we need to work on that.
"During the season we haven't conceded too many from set plays so it's really frustrating.
"Dan has been outstanding all season and he was on Saturday as well, we didn't clear the ball properly."
PNE had to dig in and adapt after Lindsay's red, switching from four at the back to five with Daniel Johnson at left wing back.
Once the numbers were levelled up though, Bauer felt North End should have been in the ascendancy and should have gone on to win the game.
With a huge game on the horizon, as Blackpool come to Deepdale on Tuesday, the squad will not be getting too down despite a disappointing result.
"I thought it was ours for the taking when they get the sending off, I thought we'd get a goal and get the three points," Bauer said.
"Unfortunately that didn't happen. Now, we have to focus on Tuesday, a big derby is waiting for us and we want to get a better result.
"After positive results we're not getting too high and after negative results we're not getting too down, but it has been frustrating because I thought we could come here and get three points.
"We just have to recover now and get ready for the big game on Tuesday.
"We know exactly what will come and we know what needs to be done to put things right.
"I definitely believe that we will give a reaction from the defeat."