Siewert was sacked as Terriers boss last Friday and Hudson - who captained Cardiff to Premier League promotion in 2013 - stepped in for his side’s visit to the Welsh capital.
It looked like the 37-year-old would leave with a point after Trevoh Chalobah cancelled out Joe Ralls’s Cardiff opener, but substitute Junior Hoilett struck a late Bluebirds winner.
Huddersfield are now second bottom of the Championship and their miserable run continues.
“I’m disappointed for the lads and for the fans who travelled. I feel the players showed togetherness to go in 1-0 down and come out and do what we did for spells. It wasn’t enough,” Hudson said.
“My focus was trying to get something for the team and setting us up to win a game of football. The players and I are disappointed, but we feel like there is something there. You could see it in spells.
“I asked them to train and play with intensity, but there is something there to spur us on and we’ve got another game on Saturday.
“If you’ve gone on the run we’ve been on then confidence is going to be low, but as soon as we turn it around you will see this team go from strength to strength because there is quality in there.
“I said before this match I want to manage this football club one day and that continues.”
Cardiff had the better of the first-half chances and went ahead when Aden Flint headed Lee Peltier’s cross down for Ralls to convert with his weaker right foot.
Chalobah levelled things up from the edge of the box when the game resumed and it looked like it would be enough for Huddersfield to earn a point.
Cardiff substitute Omar Bogle hit the crossbar, but his fellow new arrival off the bench Hoilett saw his deflected effort from a Josh Murphy pass win it.
It was a fine way for Neil Warnock’s men to bounce back from what was a disappointing 3-0 defeat at Reading last Sunday.
“We made hard work of it. It’s the biggest 2-1 I’ve ever had. We had 24 shots, but their goal knocked the stuffing out of us,” said Cardiff manager Warnock.
“We let everybody down at Reading last Sunday. That wasn’t one of my teams, but this was the best we’ve played this season.”