The average attendance at the Riverside this season is 25,618 whereas Elland Road has seen an average crowd of 25,923.
Woodgate: "I know it's not cheap getting into football grounds but how many fans do Leeds get a week two divisions below us? They get similar crowds to us.
"We have to play good football for the fans to come in.
"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.
Middlesbrough host North East rivals Sunderland at the Riverside this weekend and, like Newcastle, the Mackems have sold all their tickets.