Exeter City manager Gary Caldwell told BBC Sport:
"It was a heroic effort - it feels like we've been playing for about three days.
"With 11 men I thought the game plan worked, we bought into it, we gave up possession to a team that wants to play counter-attack and we frustrated them.
"The disappointing thing was the two goals, they were soft goals from our point of view.
"The sending off obviously has a huge impact on the game, but against 11 we dig in, the finishers come on, we really gambled in the last 10 minutes, I didn't want extra time.
"The players were outstanding. The mentality, the teamwork, the looking after each other and protecting each other in difficult moments was incredible. It's something we have to take forward.
"We have to use this performance, we have to use this feeling and take this into the next 17 games."
Nottingham Forest head coach Nuno Espirito Santo told BBC Radio Nottingham:
"It was a tough one. This is the FA Cup, we knew how hard it was going to be.
"Credit to Exeter, but probably we didn't do one of the best games.
"At the end we are happy, this is more important.
"Penalties is not a lottery. We have to prepare them and the boys were really focused on doing things properly.
"We take our penalty shots in training sessions and did really well here."