The Bluebirds, who travel to local rivals Swansea City this weekend, are currently two points away from safety in the table.
However, Hudson believes that new manager Ole Gunnar Solskjaer can guide the side to safety before the end of the season.
"I'm very, very confident we can stay in this league," he told the club's official website.
"The manager's made some good signings and added impetus. Hopefully we can carry this form and confidence throughout the rest of the month.
"He wants to play attacking football, have a lot of possession and have a go at teams. That's the philosophy he's brought in and we're just trying to put that across. We've been taking on board everything he's given us for the past month."
Cardiff have won once in their last eight games in the Premier League.