Fine build-up play from Jonathan Parr paved the way for the goal after 15 minutes, and Palace defended superbly thereafter to condemn Hull to a third defeat in four Championship games.
"The performance was excellent and we were resilient at the back," said Freedman.
"Hull threw a lot at us but I thought we coped with it and I can't remember too many clear-cut chances.
"We're not getting carried away with our start, but we've got hungry young players. We play with good intensity and always try to win the ball back, and you saw that with the goal.
"That's the sort of hunger you always want to have at your club, and going forward we have very exciting young players.
"We had that sort of attitude on Tuesday night (when Palace came from behind to score twice late on in a 2-1 win against Coventry) and we had it again here.
"We did retreat to defend the goal, but it worked for us as we sucked them in a bit. Something we've got to work on is not sitting too deep, but I think it worked for us today."
Hull boss Nigel Pearson admitted his side's lack of firepower is becoming a concern and added that he would consider changing a game plan that has yielded just two goals in all competitions so far this season.
"We did not create enough and we conceded a soft goal again," said Pearson.
"They created very little themselves, but we didn't stretch them. When you have that much possession you need to do something with it.
"We've now played three games at home (in the league and cup) and lost them all without scoring a goal, so there is cause for concern.
"I may have to change the style and be a bit more direct or perhaps I may do a bit of business (in the transfer market).
"The team are lacking confidence at home. The stats speak for themselves - our home form's been poor over the last 12 months.
"I'm still very confident we can turn it around and the club is heading in the right direction, but I understand the fans' concerns.
"The performances haven't been horrific, but we haven't scored goals and put other teams under enough pressure."
Palace took the lead when Parr outmuscled Joe Dudgeon, bustled his way to the byline and cut the ball back for Chester to poke the ball into his own net under pressure from Jermaine Easter.
Sean Scannell nearly added a second for the visitors after more hesitant defending, but Hull goalkeeper Adriano Basso produced a fine sprawling save.
The hosts should have levelled just before the break, but Julian Speroni smothered Matty Fryatt's close-range effort and Robert Koren's follow-up shot was blocked.
Speroni tipped Corry Evans' low right-footed drive round the post late on to secure the points.
Source: Team Talk
Source: Team Talk