James Vaughan hit the winner on 36 minutes to keep Palace above the relegation zone, his shot taking a massive deflection off defender Jonathan Grounds.
Mowbray said: "This was about us trying to break them down. One lapse in concentration and a huge deflection when the ball was probably going wide was enough for them.
"We didn't do enough. We were a little way short of our usual standards. My main disappointment was that we weren't good enough to score."