The Camp Nou outfit were handed the punishment by FIFA a day after they were held to a 1-1 draw by Atletico Madrid in the first leg of their quarter-final tie for irregularities found in their transfer dealings at youth level.
A transfer embargo of that magnitude would likely weaken Barca over the coming seasons, so Gerardo Martino's men will be keen to make the most of their opportunity this time around.
Costa, who has scored seven goals in six Champions League starts this season, subsequently sat out his side's 1-0 win against Villarreal in the league on Saturday and remains a doubt as Atleti prepare to host this week's return leg.
However, the hosts' home form should give them cause for optimism, having won 16 of their last 17 home games in UEFA competition.
While conceding it would have been nice to head into the second leg with a kinder scoreline, Barcelona's Xavi claims the need to win could benefit his side.
"Atletico cut down the space," he said. "It's not easy to create chances, and we have to be fluent in the game and move the ball quickly.
"It's a really tough match. We'd have liked to have gone there with a better result, but it all depends on us.
"We have to win and that benefits us because we're a team built to attack, but we are facing an opponent who is just the opposite."
