Pepe was shown a straight red card for headbutting Thomas Muller during Portugal's 4-0 thrashing at the hands of Germany in Salvador last week.
Following the heavy loss to Joachim Low's side, Portugal came from behind to salvage a 2-2 draw in their second group game against the USA, with Costa replacing the Real Madrid defender for the draw.
Paulo Bento’s men now need to beat Ghana in Brasilia and hope that Group G leaders, Germany, beat the USA to have any chance of qualifying for the last 16.
Costa is determined to keep his starting berth in the match against the Black Stars and hopes Bento will stay faithful and allow him to play over Pepe.
"I will work to help as much as possible, solving the problems we have in training and in games," he said.
"Paulo Bento is the only man who will decide who plays.
"If I play, I will give my best. If I do not play, I'll be on the bench to support our national team."
With Portugal’s fate in the hands of Germany, Costa insists that the Seleccao can still qualify for the knockout stages of the World Cup - despite the team needing to make up a goal difference gap of five between themselves and Jurgen Klinsmann’s team.
"We believe that it is possible to beat Ghana and move on to the knockout round," the Valencia defender said.
"We nurture that hope. I believe and I think everyone should believe in the team.
"We know we are a very good team that has been together for a long time and that collectively are playing very strong.
"We've had opportunities to compete in the World Cup, but the results do not demonstrate the quality of our players.
"Our players have a lot of quality and belong to a Portuguese team that is respected worldwide."