"That is the decision I have made. I am delighted to have joined Liverpool and am enjoying every minute," the paper quoted the 29-year-old as saying.
"It is a club used to winning and every time we step on to the field the fans expect to win -- that is a nice pressure to have," he added.
Asked if he regretted leaving City, who currently top the table with three wins out of three so far, Milner's answer was a short, "Not really."
"I have watched them on the TV -- I might have been watching them sitting on the bench if I had stayed at the club," he said.
The Liverpool vice-captain, who was handed the skipper's armband for Monday's 0-0 draw against Arsenal after Jordan Henderson was ruled out with a foot injury, also backed his team to keep getting stronger.
"There are very promising signs. It will take time," he added.
"We will get better and better the more we play together but to go away and play like that (against Arsenal) was pleasing."
He also praised his new team's strength in depth.
"You look down the squad list and on the bench and it is a strong balance. You need a good squad to do anything and we will definitely have that," Milner said.
"You want to be among good, experienced players and a blend of English talent and foreign players. Everything is there," he added.
Liverpool are yet to lose a game in the league so far and currently trail City by two points. The Merseyside club take on West Ham United at Anfield on Saturday.
(Reporting by Simon Jennings in Bengaluru; Editing by John O'Brien)
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