Castro stepped up from coaching the 'B' side last week after the departure of Paulo Fonseca following a run of four games without a win, and guided the side to a 4-1 home victory over Arouca in his first game in charge on Sunday.
Porto remain nine points adrift of leaders Benfica with eight games to go in the Primeira Liga, and Castro urged supporters to back the team in their final push.
"I'm expecting to go about my job every day with dedication and determination," he told the club's official website.
"I am hoping the work will be followed closely by the fans, as they are essential for development."
Porto went unbeaten last season to claim their 27th domestic title, and they face Sporting Lisbon in a crucial encounter on Sunday that could go a long way to deciding who progresses automatically to the UEFA Champions League and who will have to go through the qualifying stages.
However, with such a gap to leaders Benfica, their best chance of a trophy this season could be in the Europa League, with Castro's charges set to take on Napoli at home in the first leg of the last 16 tie on Thursday.
With two huge games on the horizon, Castro insisted it was vital his men did not look too far ahead.
"We will count our points in the end; we always look at one game at a time and that is what I try to tell the players," he said.
"We can only play one game and in the end we will see."
