Two late goals from Wolves winger Adama Traore condemned City to their first loss at the Etihad Stadium since last December.
With 16 points from eight matches, it is City’s worst start to a league campaign for six years.
They are trailing well behind Liverpool after Wolves joined Norwich as unexpected winners against City this season.
In contrast, Liverpool enjoys a 100 per cent record at the top of the Premier League thanks to eight successive victories.
Guardiola had no excuses for City’s poor performance and he was trying not to think about the advantage Liverpool have already built up.
“It was a bad day, a bad game, but we have to credit our opponent,” he said.
“Today we were not at our level. We had problems to make our game. We have faced many teams defending deep and found a solution, but not this time.
“We were not solid in our build-up. It was not just about our defence. The feeling when we lost the ball as they could run at us and that made us nervous.
“The distance to Liverpool is big, but we must not think about the eight-point gap. We are still in October and there are lots of games and lots of competitions to play in.”
– Proud Nuno –
Man City could easily have fallen behind early on as Wolves passed up three golden chances to score.
First, Patrick Cutrone skewed his effort badly wide after Traore’s pass had found a way through the heart of City’s defence.
Raul Jimenez had a pair of opportunities in a matter of minutes as he was denied by a fine last-ditch tackle from Fernandinho and then took too long to get his shot away.
Man City had started slowly and Rui Patricio was not tested until more 30 minutes had been played when he pushed away Raheem Sterling’s shot.
Guardiola replaced the ill Kyle Walker at half-time with Oleksandr Zinchenko and then sent on Bernardo Silva in place of Riyad Mahrez.
But still, his players could find no way through Wolves’ superbly organised defence.
The closest they came was when David Silva was brought down just outside the area and picked himself up to curl the free-kick against the crossbar.
As City pushed forward in numbers for a winner, they were caught on the break with 10 minutes remaining.
Jimenez danced past Nicolas Otamendi and squared for Traore to slot past Ederson for his first Premier League goal since September 2018.
And then with virtually the last kick of the game, Traore repeated the trick as he ran clear to seal a famous win for Nuno Espirito Santo’s team.
“I’m very proud. It was a very good performance and the work from the players was outstanding as it is very difficult to play against City,” Nuno said.
“The first thing you have to do is stop them and we did that because the players were running like crazy.
“Adama did well for his goals but all the players did well. I have to congratulate them today.
“But now we have played like that, the challenge for the players is they have to sustain this level.”