The fifth round tie on Monday night finished 1-1 after extra-time and went to penalties, where Forest won the penalty shootout 5-4 with Matz Sels saving from Jack Taylor.
Before then, Ryan Yates' goal had canceled out George Hirst's opener for Ipswich.
Nuno later said of the home fans: "The help they gave us in the penalties trying to distract Ipswich players, we thank them a lot.
"The players did their job quite well. We compete well. The first half was flat for both teams. I'm really happy that the boys achieved it and our fans are happy tonight."
On being one step closer to Wembley, he added: "Now it is game by game. We have City then we can focus on the FA Cup. It is a competition we love and we will do out best."
On Matz Sels' shootout save: "In the end it was beautiful to see."