Speaking at the club's annual general meeting, Petrie urged supporters to return to Easter Road to avert the potential for a second successive annual financial loss after recently reporting a second loss in eight years.
"Growing the attendances by Hibernian supporters is our core strategy," the Hibs chairman said.
"We are asking supporters to do what you do best - support the team at home matches. If we cannot do that, and if we cannot grow our income, then the only route to get back to break-even will be to make substantial reductions in costs.
"The club is asking shareholders, supporters and everyone connected with the club to play your part in getting back to where we all want it to be."