League One City brilliantly responded from two goals down after 38 minutes to dump the Barclays Premier League leaders out of the FA Cup.
Chelsea reject Filipe Morais levelled the fourth-round tie with 15 minutes to go and Jon Stead, the scorer of City's first, teed up Andy Halliday for the winner eight minutes from time.
And substitute Mark Yeates tucked in a stoppage-time fourth to inflict the Blues' first home loss this season and spark jubilant celebrations from Phil Parkinson's visitors.
Mourinho on Friday said it would be a "disgrace" if his side lost.
After Chelsea's hopes of challenging for an unprecedented quadruple were ended, he said: "In this moment I feel happy for them
I could find in my bad feeling with the game and with the result space to feel happy for them
"By another side I feel ashamed and I think the players should feel exactly the same as I feel.
"By one side this is the beauty of football, the beauty of the FA Cup
It happens more in the FA Cup than any other country.
"(But) I repeat the word that I used yesterday in case we lost - it's a disgrace
A sporting disgrace, but it's a disgrace.
"I know in the history of this competition it happens to every team now and again.
"For me it's the first time and I think it's unacceptable to lose against a team from a lower league."
Bradford manager Phil Parkinson believes his side's triumph at Stamford Bridge will live long in the memory and hailed the performance from his League Two outfit.
"It's incredible, especially after being two down," he said on BBC Radio Five
"The lads are absolutely bouncing in that dressing room and what they've done today will be remembered for a very long time - not just in Bradford but all around the country.
"When we got to Wembley (for 2013 League Cup final) by getting the result at Villa Park, it was a day we'll never forget, and we've had some terrific ones, but playing the league leaders and one of the best teams in Europe and scoring four goals..
That's going to take some beating.
"The first 20 minutes I was pleased
I thought we did well
We conceded a goal from a set-play and then we gifted them a second, but obviously getting that goal and coming in just 1-0 down and still being in the game was so important.
"We played with so much belief kicking towards out fans in the second half
We really took the game to them and for long periods I thought we were the better team
We had a few moments when we were chasing the game but in general we played really well and I couldn't be prouder."
When the score was level at 2-2, Parkinson admitted the thought of playing for a draw had never entered his mind.
"We certainly weren't going to sit back because the way the lads were playing, we're a better team when we're positive in our division and at any level," he said.
"We made one or two changes but they weren't negative changes - they were just fresh legs, really, and we just kept on attacking
The goals were of real quality and Jon Stead scored one and made another couple, but the all-round team performance was excellent."
Source : PA