Forest thrashed the Hungarians 4-0 on Thursday night.
Keane said afterwards: "Very difficult, but we knew that before the game. We were playing against a Premier League team, and they were full of quality. So it was always going to be difficult.
"We are disappointed because of the goals we conceded more than anything – an own goal, and for the second goal, we gave the ball away. The fourth was a penalty, so it's not like they cut us open really.
"But in terms of play and quality, they are way ahead of course, there's no question about that. I'm just more disappointed with the mistakes we made."
The Irishman also said: "It was just the decision-making today, but it's a different level, and you could see that. I thought we might get one goal, but it didn't happen, we hit the post and the crossbar.
"Then you look at the players they bring on, Morgan Gibbs-White and Callum Hudson-Odoi – it just goes to show the levels and the quality.
"We completely over-achieved. Being unbeaten we wanted to keep that as long as we can. But I couldn't be more proud of the boys and the journey they have taken, but we always knew it was going to be a massive task tonight."