Forest had the lead via Chris Wood only for Bournemouth to equalise through Antoine Semenyo.
Nuno later said, "I'm disappointed with how we concede, we had the game under control. It was a tough game, a good game, both teams had momentum. We could have had more.
"We don't know exactly (on the extent of Danilo's injury), we know it's serious. It's unfortunate for him as he is a nice boy, in a good moment. We are going to miss him.
"I think we have a good squad that allows us to have options coming from the bench. But we are going to miss Danilo because he is a top player.
"Chris Wood did well, he gives us another option. Overall I am happy. It's the first game of the season. I am satisfied with the way we played and competed against a tough team. It was a good game, they had chances, we had chances. Let's go for the next one."