Hammers captain Jarrod Bowen swapped goals with Brentford striker Igor Thiago as the two teams finished extra-time at 2-2.
In the shootout, Dango Ouattara fluffed his Panenka attempt for Brentford, so seeing West Ham win on penalties, 5-3.
Nuno said afterwards: "We are happy, we are delighted, that we achieved what we proposed to do. It was a tough match but it was a fantastic atmosphere, the London Stadium is helping us so much, so I think we deserved to give this moment of happiness to our fans.
"We started well. It was a very tight game, Brentford are a very good team but in the second half we had the chances to put the game to bed, but the final pass or the final combination didn't come through. Then we allowed the transition for Brentford which put us with 30 minutes and then penalties. The answer of the squad was good, we made a lot of changes and the players that came in helped, so it's positive.
"I believe the FA Cup helps in terms of motivation, in terms of everybody being switched on, knowing that they are going to have the chance to play. During the week many of the players work very hard and then we cannot reward them in the game and sometimes it is unfair. Having the FA Cup alongside the situation in the league will help the squad work even more and compete even more, we need all the players."
On Crysencio Summerville's injury concern, Nuno added: "Let's assess him. He felt a knock. I don't know exactly what he has. It is concerning but hopefully we recover with this moment of joy. We'll get better, we'll be faster and we will be able to compete against City.
"Enjoy for a couple of hours and then refocus, recover well and respect your body. It was a big effort from a lot of the players. Then we have to go again."