United were disappointing once again as they scraped a 2-2 draw in 90 minutes, as Marouane Fellaini rescued the 10-man hosts - who had Sergio Romero sent off - deep into second-half stoppage time.
Prior to Fellaini's header, Jack Marriott had seemingly given Derby the win with an 85th-minute goal which added to Liverpool loanee Harry Wilson's gorgeous free-kick, cancelling out Juan Mata's early opener.
Penalties were the least Derby deserved and the first 15 spot-kicks were accurate, before Jones stepped up and saw his feeble effort easily saved by Scott Carson.
As the shoot-out progressed towards defenders such as Jones and Eric Bailly, Mourinho acknowledged that he did not have a huge amount of faith.
"I repeated what I said in the last match, that their [the opponent's] dressing room was one with belief, because it [the match] was open and they played quite well," Mourinho told Sky Sports.
"We needed to go and kill the game, which we didn't. We couldn't be dominant in the beginning of the second half and only after the equaliser we had that reaction, which I don't like.
"Hey lads, we can go home now!"— Carabao Cup (@Carabao_Cup) September 25, 2018
After 15 successful spot-kicks between both sides, Scott Carson decides enough is enough. pic.twitter.com/dwwUF8WFpb
"I prefer to be proactive, but then we go for it only after the 1-1 and after the red card we are in a little difficulty.
"With one less [player] there was a reaction of pride, of a group that didn't want to lose and tried until the last second.
"Then penalties come and someone has to miss. When I saw [the penalties] going after the sixth, seventh [takers], I knew that we were going to be in trouble with Jones, with Eric. I knew we'd be in trouble again."
A prickly Mourinho then took offence to his interviewer suggesting he had been critical of United.
"You think I criticise? I don't think so," Mourinho said. "That's not criticising the team, I belong to the team.
"I don't think you are correct when you say I'm criticising. Do you want me to analyse or go away?
"You want me to say we play a phenomenal match? The truth is the opponent in the second half started better than us and we weren't able to match that intensity."