Jose Mourinho was "ashamed" by Chelsea's "unacceptable" FA Cup fourth-round exit, but praised Bradford for their giant-killing act in a 4-2 win at Stamford Bridge.
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. I'm honest.
"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."
Mourinho expects Chelsea to be lambasted for their display.
He said: "If I was you (the media), I would be very critical with Chelsea, with Chelsea manager, with Chelsea players, but not just that because I think the other guys don't deserve that we forget them. They deserve (praise) after such an impressive result."
Mourinho made nine changes following the midweek draw at Liverpool, and with next Tuesday's Capital One Cup semi-final second leg in mind.
He defended his team selection.
"The team I select is a good team," he added.
"When we go to the other players, the other players have to be ready to play for Chelsea, to play any game.
"If they cannot play against a team form the Championship or League One or League Two, what do we do? I think the selection was good enough."
Andre Schurrle was conspicuous by his absence from the matchday squad, having been a peripheral figure this term and linked with an imminent exit.
Mourinho on Friday said the World Cup winner would start, but his omission - officially due to a minor muscular injury and the forward did sit behind the dugout with other non-playing squad members - sparked suggestions the "phenomenal" offer required to seal his departure had been received.
The Portuguese insisted Schurrle was merely injured.
"He arrived this morning saying he has a little pain in the back," the Blues boss added.