Castro was promoted from the B team to replace Paulo Fonseca, who was sacked last week.
The 52-year-old guided the Dragoes to a 4-1 home victory over Arouca on Sunday in his first game in charge.
The outcome allowed third-place Porto to halt a four-match winless run and close the gap on Sunday's opponents Sporting, who are second, to two points.
"I know this job carries a lot of responsibility," Castro said. "FC Porto has great tradition in terms of victories.
"We are one of the best clubs in the world in terms of titles and as such, this adds to the responsibility.
"But we want to end the season in the best possible way and try to win titles."
Castro insists there is no chance of him fielding a weakened team against Napoli despite their important meeting in Lisbon this weekend.
Castro refused to prioritise the competitions his side are involved in, while stressing how seriously he is taking the challenge of their Italian visitors.
"We are focusing on one game at a time," Castro said. "To talk about the Sporting game is premature as we have a big game ahead of us on Thursday against Napoli."
Ricardo Quaresma, who scored twice at the weekend, is expected to lead Porto's attack.
The Italians travel to the Estadio do Dragao on the back of Sunday's 1-0 triumph over Roma.
The outcome allowed Napoli to strengthen their hold on third place in Serie A and close the gap on Roma, who are second, to three points.
Despite the high spirits in the Napoli camp, club coach Rafa Benitez has warned his players to brace themselves for a difficult challenge in Portugal.
"Porto are a very strong team," Benitez said. "The atmosphere will be very difficult to deal with when we go to their stadium, it will be a very difficult test."
The visitors will be bolstered by the return of midfielder Valon Behrami, who missed the encounter against Roma with a muscular injury.
The return leg takes place at the San Paolo stadium on March 30.