After a disappointing defeat against the Saints in the Premier League, Roberto Mancini's side returned to form with a classy display against Leeds to move into the last eight
The 2011 winners cruised to victory with a much-improved display after their surprise Premier League loss, which saw them slip 12 points behind title rivals Manchester United.
Toure opened the scoring for the hosts inside five minutes, giving Roberto Mancini's side the perfect start, and the Ivory Coast star believes they responded well to their defeat on the south coast.
"I think [we reacted well], because in the first half we played very well, giving pressure to Leeds,” he told ESPN.
"We know [Leeds are] a very tough team, they play very good football and they are physically strong. I think today was a good response from Man City."
Milner, who earned a start against his former club, echoed the sentiment of his fellow midfielder, insisting that the FA Cup is as important as any other trophy and it was vital to get back to winning ways.
"It's another trophy," he said. "We want to win every game we step out on that field, and obviously, like we said before, we knew we needed to improve from last week.
"We did that, kept a clean sheet, which is important as well, and scored four goals, so that's pleasing."
Milner came through Leeds' academy and grew up supporting the Championship club but claimed it had no impact on his performance against his former team.
"Once you get on your field it's just another game," he added. "It was a good atmosphere; the travelling fans made a lot of noise and it was a good result for us in the end."