Guardiola hopes the 27-year-old can play an influential role as City bid to chase down Liverpool in the Premier League title race.

The City manager said: "I said many times how important Kevin is for us. Without him, last season would maybe not have been possible.

"So far we have done incredible in terms of results, but we have an opponent (Liverpool) that has done better. Fifty points is incredible, it is huge.

"But they are an opponent that has done better than us without him.

"Now he is back he will be fresh in the mind and the legs, and is going to help give us extra in the creativity in the last third, in the fight. Today he was our captain and he showed us why."

City brushed aside their Championship opponents. Raheem Sterling, Phil Foden and a Semi Ajayi own goal put the hosts into a comfortable half-time lead before further efforts from Gabriel Jesus, Riyad Mahrez, Nicolas Otamendi and Leroy Sane completed the rout.

"We took (it) seriously," said Guardiola. "We do what we have to do to become a great, great club.

"The great clubs don't choose competitions, don't choose games. Every game you have to do your job and we did amazingly again."

Foden's goal – his first at the Etihad – did not come from the cleanest of touches but his general play impressed Guardiola.

The Spaniard said of the 18-year-old: "Today was fortunate. He wants to control the ball and it touches his knee and goes in, but he was there and his movement was incredible.

"He still has to improve but that is normal. He is 18 years old and the best way to learn is to play."

Asked if Foden might be loaned out to gain experience in January, Guardiola said: "No way – impossible."

Rotherham manager Paul Warne felt no shame in defeat.

Warne said: "I was pleased the final whistle went. We came across, obviously, a very good Manchester City team who wanted to win.

"I think the first 10 minutes confused my lads a bit. We'd prepped them as well as we could but I don't think (you realise), until you actually witness it with your own eyes, how quick they are and how good their movement is.

"The gulf in class is there for everyone to see. It summed it up when I told my right-back to smile when Sterling came off and Sane came on. I was thinking, 'Oh my God'."

Some of the build-up to the game focused on Warne's resemblance to Guardiola.

Warne said: "I spoke to him beforehand and said, 'be gentle' but after I just shook his hand and said, 'your team is a joy to watch'."

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