Leeds have won just once at home since returning to the Premier League and have lost two of their last three games at Elland Road.
They did manage a point against Manchester City at home, but their record means they have garnered only four points from four league games at home in the ongoing campaign.
Parker insisted that such a poor run cannot continue and Leeds need to get back to a place where Elland Road is a fortress again.
He pointed out that Marcelo Bielsa’s success at Leeds has been based on their terrific home record and believes that needs to happen in the Premier League as well.
The former Leeds star stressed that improving their home form will lessen the pressure on the players to get extra points when they are on the road.
Parker said on LUTV: “Make Elland Road a fortress again and get back doing what we were doing well.
“The success based over the last two-and-a-half years under Marcelo is the form at Elland Road.
“We were so hard to beat, yes the fans make that, but it is getting that fortress back.
“Once we keep picking up points at home, then it just frees yourself going away and there is no pressure to get those points away from home.
“It is going to be an up and down kind of season for a lot of teams, but we can get some consistency into the game by picking up results at home.
“We should be more than comfortable to get to that middle of the table.”
Leeds have a tough test at Elland Road lined up for Sunday when Mikel Arteta’s Arsenal outfit visit in the Premier League.