كتب : Omar AbdelAziz
The Serie A leaders were condemned to an embarrassing 3-1 defeat at Atalanta on Sunday, but have now booked a place in the cup's semi-finals at the expense of the holders.
"This win was a very good reaction to the defeat we suffered last Sunday in Bergamo," Mourinho said on Sky Sport Italia.
"Everything is better, on and off the field, when we put in that kind of performance.
"I'm happy and so are the players because we really don't like losing games. We also attached a lot of importance to this competition."
Mourinho paid tribute to 18-year-old defender Davide Santon, who made his Inter debut at San Siro.
"It's never easy to make your debut against Roma, but he was fantastic," added the Portuguese.