The Catalans trailed the Rossoneri 2-0 from the first leg, but were able to reach the quarterfinals of the Champions League thanks to a superb Camp Nou showing on Tuesday.
“I am so proud to have been part of one of the great comebacks,” he told the club’s official website.
“It was one of the best games I've experienced. It was the day and the match that we needed. We have been unlucky when seeking other comebacks.
"I have always thought that those are the greatest things and now we can say that we got one too.”
Busquets also claimed that the side did not feel any extra motivation to silence doubters after a recent run of indifferent form, with the players just focusing on the task in a professional manner.
“We didn't do it because we wanted to silence the critics, we did it for ourselves. We’re professionals and we like that,” added Busquets.
“Most of us are locals and so it’s especially intense for us. You have a bad time when you lose, so these days have done a lot of good for our confidence.
"But neither did people need to take the situation quite as seriously as they did. All teams have drops in form.”
A Lionel Messi double alongside strikes from David Villa and Jordi Alba were enough for the Blaugrana.