The Ivory Coast midfielder opened the scoring in the fifth minute before Sergio Aguero scored either side of a Carlos Tevez goal as the Premier League champions booked a quarter-final fixture with Barnsley for early next month.
The win comes after last weekend's league defeat to Southampton and Toure was delighted with the response.
"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."