Carden told BBC Radio Cambridgeshire: "As part of the management team I've always tried to respect our opponents.
"David showed a lack of respect to Martin Ling, John Schofield and myself by saying we looked unfit and weren't doing the right things over Christmas."
While Livermore was generally positive about the U's, he felt the Stutes' cross-city rivals looked under-prepared for their 5-1 defeat to Mansfield.
After the match, Livermore said he thought the U's failed to show the same desire as his side.
We HAVE to be putting teams like Histon, away at home comfortably
"When you make comments like that it can come and bite you on the backside, so maybe it's something David needs to learn," Carden said.
"It's not nice when you hear managers who haven't done much in the game coming out with that and after losing 6-1 [to Grimsby] on Monday maybe he's eating his words a little bit."
U's have come under pressure from their supporters following a disappointing Christmas period which yielded just four points from a possible nine.
Carden says he can understand the fans' frustrations, but has called on them to continue backing the side.
"I can understand where they are coming from as they want to see their team being successful," he said.
"I suppose it's easier to criticise than be constructive, but everyone wants to push on and we need the fans as that 12th man."
Source: BBC Sport