The visitors pulled one back with a penalty but it proved a minor setback for City, who again dominated Southampton in the second half.
"The team showed me some signals that in some positions we are not stable enough", the City boss explained to The Independent, specifically referring to set-pieces.
"We were brilliant at times".
There were moments of encouragement for Saints after that time.
And Alvaro Morata also found the net twice as unbeaten Chelsea defeated Crystal Palace 3-1 to move to second on the table, two points behind the league leaders.
Sane, returning to the side in place of Riyad Mahrez in City's only change from the 1-0 win at Tottenham Hotspur on Monday, fired in a low cross which Hoedt could only divert into the roof of his own net from under the crossbar.
Southampton had the minor consolation of becoming the first team in 630 minutes to score against City but the leaders' form is ominous for the rest of the division.
And it will now be seven Premier League games without a win following their visit to the Etihad.
Guardiola was asked if Sterling can now be considered amongst the world's best players, but replied that the England global still has work to do to be ranked as such.
Sane has so far scored three goals and provided four assists in 13 appearances for City this campaign. The game was not over.
While numerous bottom sides could be considered the "usual suspects", the sight of Sean Dyche's Burnley - who finished seventh with 54 points last season - is a little surprising. Unbeaten Chelsea made a slow start but Morata cheered the Stamford Bridge crowd by putting his side in front from close range in the 32nd minute after pouncing on a cross by Pedro.