Leverkusen, who face bottom-placed Real Sociedad, are currently third in Group A and need Shakhtar to drop points at Old Trafford to stand any chance of progressing to the next round.
Castro is hopeful that his side can do their part by building on their impressive away victory over Borussia Dortmund at the weekend, but he acknowledges that the situation is ultimately out of their hands.
"We simply have to build on what we did in the Dortmund game and give it everything we've got. And then we have to hope Man United help us out," he told reporters at a press conference.
A draw with Sociedad is unlikely to be enough for the German side, who are currently one point behind Shakhtar but have a much worse goal difference than the Ukrainians.