The Bluebirds dropped to fourth in the league as their star-studded followed up their 2-0 loss by Ipswich with a 1-0 reverse at Selhurst Park on Tuesday.
Now club captain Hudson insists Cardiff must turn their stuttering Championship form around against Barnsley on Sunday.
"We know we have to go and win that game," admits centre-back Hudson.
"It is a game we should be getting three points from, whether we lost these two or won these two."
Cardiff boast one of the Championship's best squads including a high-quality strike-force of 15-goal England international Jay Bothroyd, Wales star Craig Bellamy and ?4m man Michael Chopra.
While their ammunition is provided by Seyi Olofinyana, Stephen McPhail and Jay Emmanuel-Thomas and last season's Championship top-scorer Peter Whittingham.
But Dave Jones' men have lost three of their last five games as the Welsh club bid for a top-flight return after 39 years in the lower divisions.
"We're not happy with the way last two games have gone but have ten games to put them right," said defender Hudson.
"We need to start winning games if we are going to get promoted automatically - starting against Barnsley.
"But I don't think we have felt the pressure, the way we played suggests that it has not affected us.
"The only pressure we have is on ourselves as we should be doing better. Mistakes have just cost us."
Cardiff dominated Ipswich in their Championship defeat to Ipswich on Saturday as Whittingham, Chopra, Emmanuel-Thomas and Bellamy were denied by keeper Marton Fulop while Dekel Keinan had a goal disallowed and Whittingham hit the post.
Whittingham also missed a penalty in their loss at Crystal Palace while Emmanuel-Thomas and Keinan hit the woodwork before James Vaughan had a goal disallowed and Kagisho Dikgacoi scored late on for relegation-threatened Palace.
Dikgacoi's strike was due to some lapse defending as Pablo Counago's hooked pass dropped over the Bluebirds back-line and Dikgacoi's scuffed shot, under Paul Quinn's challenge, rolled into Cardiff's net.
"We are disappointed," said Hudson, whose Cardiff side had lost just once in the league since New Year's Day before their current poor run.
"A midfielder runner has come in free and it is disappointing from our point of view. It is a problem that needs to be looked at."
But Hudson, a former Palace player, was quick to console Whittingham as the former Aston Villa winger squandered a chance to put Cardiff in front at Selhurst Park - before Palace's late winner.
"He has pulled us out of games that we didn't think we'd win a number of times over the years," said the 28-year-old.
"And I'm sure he'll take the next penalty because his quality is undoubted and I'm sure he'll stick the next penalty away.
Source: BBC Sport
Source: BBC Sport