However, Guardiola still took pride in City's performance and urged his side to usurp Jurgen Klopp's men, who took a one-point lead in the title race with a 4-0 win at Bournemouth earlier on Saturday.
"I said that is not going to happen. We are not here to be invincible, we are here to be champions," said Guardiola.
"We are calm, we move forward, it is part of the competition. There is no sport in the world: tennis; basketball; golf that one team win always. When people are saying that they are selling an illusion.
"It's part of the competition. You can lose, but it is how you lose."
City lacked the cutting edge of the injured Sergio Aguero up front as despite dominating the first-half, they failed to profit with Raheem Sterling and Leroy Sane missed big chances.
The visitors were then hit with a sucker punch right on half-time when N'Golo Kante fired Eden Hazard's pass into the roof of the net with Chelsea's first serious attack.
And Guardiola warned that City's dreams of winning the Champions League for the first time this season could end in similar fashion if they don't learn to kill games against the toughest opposition when they are on top.
"That is the Champions League level. People say Man City are favourites for the Champions League. That is what is going to happen in the future on the biggest stages, but the way we played today is absolutely incredible."
Chelsea ride their luck
Chelsea boss Maurizio Sarri had lost all of his previous three meetings against Guardiola and was growing increasingly frustrated at his side's inability to hold possession as the visitors dominated the first half.
But after two defeats in their previous three league games, Chelsea bounced back in style as they went onto have the better of the second period after the boost of Kante's opener.
"We won today but we have to say we were a bit lucky in the first 25 minutes," said Sarri.
"We played very well in the last minutes of the first half and the first 20 minutes of the second half.
"I'm very happy because we know it is not easy to win against Man City in this moment.
"For me is not easy to win against Guardiola. Now we have to find this kind of motivation and need to play with this level of determination and aggression in other matches."
Sarri's decision to field Hazard as the focal point of the Chelsea attack and maintain Kante in an advanced midfield ultimately paid off.
The Italian has resisted calls to return Kante to the deep-lying midfield role where he shone in winning the World Cup with France and Premier League titles for Leicester and Chelsea at the expense of Jorginho.
And when Hazard was finally fed the ball to feet inside the City box, his pass picked out Kante, who side-footed the ball high past Ederson.
"Sometimes, I have chances in this position to score. I reacted, got there and had a shot and I’m happy to score," said Kante.
Ederson had been a spectator before picking the ball out his net, but was called into action again to keep his side in the game just after the break when he palmed away Willian's free-kick.
Willian wasted another good chance on the counter-attack as having been behind only once before in the Premier League this season, City were rattled and rarely threatened to get back in the game in the second period.
Defending set-pieces has often been a rare Achilles heel for City and it was exposed when Luiz made the game safe by rising highest to Hazard's corner and looping a header in off the underside of the bar.