The defender praised the team’s impressive display as Leeds secured progression to the next round.
The triumph also marked their second win over Forest in just four days, following Saturday’s Premier League success.
“It was great,” Elvedi told BBC Radio Leeds.
“It was just fun today. I am just proud of this team with this performance.
“I think we deserve this win tonight. Very, very strong performance from the whole team and, yeah, happy going through to the next stage.
“I had a hard battle. It wasn’t easy but I like it when the player is strong and I think I did it well. Still things to improve but for the first game it was okay.
“I am just happy to be here. There are great teammates. It was very easy to come here to this club and every day it is fun to go into the training and to be on the pitch with these good players.
“The whole team is just amazing. We have a lot of people who speak German so it makes it easier for me.
“But also the players who speak English, it is just easy for me to be in this group. I am happy when I am on the pitch.”