Pierre-Emerick Aubameyang had a penalty saved after Kostas Mitroglou scored the only goal, and Benfica goalkeeper Ederson turned in further heroics to preserve a slender advantage for Rui Vitoria's men.
Nevertheless, Castro is confident Dortmund are fully in control of their own destiny heading into Wednesday's return at Signal Iduna Park.
"We're favourites," the 29-year-old told a pre-match news conference. "We saw in the first leg that we were clearly the better team.
"Now we have to be aware not to concede a goal at home, because then it gets more difficult.
"We do know that it is very important to be mentally strong, but we are well prepared for this, in particular if you see our last performances.
"Benfica have a good defence. Nevertheless we created a lot of chances in the first leg.
"We have to look at our own team. Everything else is secondary.
"Benfica can always score out of nothing. We'll have to consider that in our tactical approach to the game."
Thomas Tuchel's side were in emphatic form as they dispatched Bayer Leverkusen 6-2 in the Bundesliga on Saturday but the joy of victory was checked by the all-too-familiar sight of Marco Reus limping out of the action with a thigh injury.
"Marco Reus was in a fine form," Castro said. "It's a set-back. But we also have a lot of players that can replace him."