The sight of empty seats has become an uncomfortably regular sight for the club who only four years ago were enjoying average crowds of 32,000.
Woodgate said: "We have to play good football for the fans to come in.
"I know it's not cheap getting into football grounds but how many fans do Leeds get a week in a division two below us? They get similar crowds to us.
"The manager wants us to play flowing football, we enjoy playing it more, and that's how we are aiming to build.
"Hopefully we will bring in more fans by the football we play.
"We only had 23,000 fans in for the Birmingham game, probably because we had not been playing well, but we had a good performance in that game so hopefully they will start coming back.
"I know it's expensive but a lot of football stadiums are expensive."