The Citizens progressed to the quarter-finals of the world's oldest domestic football competition courtesy of a comfortable 4-0 win at the Etihad Stadium.
"I hadn't played against them before but once you get on the field it's just another game," Milner, who began his career at Leeds, told ESPN. "It was a good atmosphere and a good result for us in the end.
"It was important we bounced back, they've knocked a few Premier League teams out of cups this season so it was important we did a job and we did it well.
"We had to improve on last week, we did that, we kept a clean sheet and scored four goals so that's pleasing."
City have won the FA Cup on five occasions - in 1904, 1934, 1956, 1969 and 2011.