Will Grigg produced the second-half winner to send City out of the competition.
Cook said: "It feels great. It's such a severe test. They're such a strong side and move the ball so well. We had to ride our luck at times and the sending off is always a big incident.
"Our lads deserve credit for their work and some of the blocks they made were outstanding and to beat Man City you have to do that.
Cook was involved in a halftime fracas with City boss Pep Guardiola, but he added: "There's no problems, from our point of view we're trying to get every edge and everything we can and from his point of view he wants the game played and he's a fantastic manager.
"It's a great night for Wigan."