With the spotlight off them, Chelsea moved just two points behind long-time Premier League leaders Liverpool, with a 2-1 win against Brentford.
Wolves sacked Gary O'Neil after a fourth straight defeat while Southampton axed Russell Martin following a 5-0 hammering by Tottenham.
AFP Sport looks at three talking points from the Premier League weekend.
Answers elusive for Pep
It is difficult to argue that City are now experiencing a full-blown crisis.
Guardiola signed a new two-year contract last month at a point when City had lost four in a row, saying he did not feel he could leave the club at a difficult time.
Now he is facing questions as to how -- and when -- he can stop the rot after a painful 2-1 defeat to United, who had won just one of their first four league games under Amorim.
Guardiola provided a harsh self-assessment after the defeat, which came courtesy of a Bruno Fernandes penalty in the 88th minute and an Amad Diallo winner two minutes later.
"I'm the manager and I'm not good enough, simple as that," he said.
Midfielder Bernardo Silva was even harsher, comparing City's collapse in the final minutes to an under-15s team.
City have matches coming up that look winnable on paper -- against Aston Villa, Everton and Leicester -- but with every defeat the scale of Guardiola's task looks more daunting.
Two-horse race?
Earlier this month Liverpool had a nine-point lead at the top of the Premier League -- now it is down to just two.
Enzo Maresca's Chelsea have won their past five games to close the gap on the Reds, who still have a match in hand.
Liverpool showed impressive strength of character to twice come from behind for a 2-2 draw against Fulham on Saturday despite playing the bulk of the game with 10 men.
But their momentum has slowed, with the Fulham result following a 3-3 draw last week against Newcastle.
Free-scoring Chelsea have taken full advantage, climbing above London rivals Arsenal, runners-up in the past two campaigns, to stake their claim as Liverpool's main challengers.
The Blues finished last season strongly under former manager Mauricio Pochettino but few expected Maresca to master his brief so quickly.
The Chelsea boss is eager to say they are not in the title race but the table suggests otherwise.
O'Neil, Martin axed over relegation fears
Gary O'Neil and Russell Martin paid the price for their clubs' Premier League struggles.
Martin's sacking was announced shortly after a sobering defeat to Spurs, who scored all five goals at St Mary's in the first half on Sunday.
Wolves suffered a damaging 2-1 loss to relegation rivals Ipswich at Molineux on Saturday, after which O'Neil said he was struggling to help his team cope with the "real basic stuff".
Wolves, second from bottom of the table, are five points from safety.
But their plight is not as perilous as that of Southampton, who are staring at an immediate return to the Championship.
Martin departs having taken just five points from 16 games, leaving Southampton nine points adrift of safety.
