Two saves from goalkeeper David Marshall secured a place in the May 22 final at Wembley after a 3-2 defeat on the night had left the tie balanced at 3-3 on aggregate.
"You can't single anybody out. Marshall will take the plaudits for penalty saves, but every player was magnificent," said Jones.
"We will make mistakes, but we don't half respond when we do make them. They showed a lot of bottle. I'm proud to be manager here and appreciate how far we have come."
After winning the first leg at the Walkers Stadium 1-0, the Bluebirds appeared to be set for a straightforward route when they took the lead through Michael Choprea.
But the visitors hit back to lead 3-2 on aggregate and it needed a Peter Whittingham penalty to take the tie to a shoot-out which Cardiff eventually won.
Goals from Matty Fryatt and Andy King, coupled with an own goal from Mark Hudson, had given the Foxes the advantage.
No goals were scored in extra-time and everyone had scored in the shoot-out until substitute Yann Kermorgant tried an audacious chip that was saved by Marshall.
When Marshall also saved from Martyn Waghorn the Sunderland loanee sank to his knees as Cardiff prevailed 4-3 in the shoot-out.
"It's tough on the players. I think our performance epitomised us this year. I think the commitment, desire, application was first rate. I can't ask a great deal more," said Nigel Pearson, the Leicester boss.
"Once you get to a penalty shoot-out it's about dealing with it and they've been better than us in it. There are a lot of very, very disappointed players in there and although the emotion's a bit raw at the moment, I'm proud of what they've achieved this season."