After being shown a red card for a headbutt on Thomas Muller in Portugal's 4-0 FIFA World Cup Group G defeat to Germany, Pepe was forced to sit out the 2-2 draw against the United States, with Costa stepping into the breach.
Realistically, Portugal will need group leaders Germany to beat the USA on Thursday to have any chance of qualifying for the second round.
That would leave Paulo Bento's men, whose match against Ghana kicks off at the same time, needing to win and overcome the goal-difference gap of five that exists between themselves and the Americans.
And Costa is determined to play his part in the crunch tie.
"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."
The Valencia man is confident Portugal can qualify for the last 16, despite setbacks in their opening two fixtures.
"We believe that it is possible to beat Ghana and move on to the knockout round," he added. "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."
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