With the scores locked at 2-2 after extra-time, Forest goalkeeper Matz Sels was the hero as the visitors won the shootout 4-2.
Afterwards, Nuno confirmed a broken nose for goalscorer Taiwo Awoniyi.
He also stated: “We are relieved, I think we all are. It was not the best game. We started bad but reacted well. In terms of the first half, we were really dominant, created and changed the score.
“The idea in the second half was to try to close the game down. We conceded from a set-piece and after that everything changes with the crowd.
“Exeter were one man less, so a lot of credit for them because they didn’t give us any space and made us rush decisions. We are relieved and happy that we go through.
"There are no starting players or substitutes, it is a squad that we will use to face all the competitions that are ahead of us.
“It is not about resting players, it is about rewarding the players who are working so hard. Many of them are coming into games and having so much impact, so why not change things around?”
On facing Ipswich at home in the fifth round, Nuno also stated on his selection plans: “I cannot say, let’s see. But since we started the competition, this was our idea - to try to create a platform for our players to have game time and help us moving forward for the rest of the season.
“If everyone has minutes in their legs, it will make things easier for us (in the Premier League) - I hope. As long as we are healthy and have enough numbers, I think we can compete in both competitions really well.”
On Exeter, he concluded: “Wow. We took a look at them (beforehand) and knew it was going to be hard. They fought for their lives.
“I have been on the other side, as an underdog, many times so I know how hard it is. I credit Exeter a lot.”