The Blues were swept away by Pep Guardiola’s City on Saturday evening, with the Citizens scoring three goals inside the first 40 minutes - including two in the first 12 minutes.
Many fans left their seats as soon as Raheem Sterling tapped home from yet another David Silva assist but Allardyce says the Blues squandered the chance to claw their way back into the game before it got out of hand.
Speaking in his post-match press conference, the 63-year-old boss said: “The biggest turning point in the game was a cruel blow for us on the header that was missed by Yannick Bolasie and then the poor defending one minute later from the goalkeeper’s restart.
“They were two-nil up, that was the biggest turning point in the game.”
He added: “I think that, then, you’re two-nil down so early on and then you try and get back in the game because you’re going to panic a little. Then, we opened ourselves up too much and we concede the third from a counter-attack.
“It shows that no matter what you do, Manchester City can break you down - whether you shut them down from the front or whether you drop in your own half and leave ten men there - no matter what you do, they’re good enough to break you down.”
“We got better”
The Blues did, however, restore a modicum of pride thanks to Bolasie as he struck just after the hour mark to get the hosts on to the scoresheet.
“We got a lot better in the second half and as the game went on, we tried to get ourselves back in the game,” Allardyce stated.
“Yannick gave us a lift with his goal but in the end, they’re such a wonderful side that, for me, the second-half was making sure we didn’t get beat by any more.”
Allardyce opted to start two strikers, with Dominic Calvert-Lewin supporting Cenk Tosun, in a move seen by many fans as perhaps too attacking against a dominant side like Guardiola’s Citizens.
When quizzed on his team selection, the Blues boss answered: “We were struggling for players in midfield but I’d say it was more about our choices in the first-half. Our choices became a little disorganised because we went two-nil down so early on.
“Playing a team of this quality, you cannot afford to miss the big and best chances of the game.”