Forest skipper Morgan Gibbs-White struck after Ollie Watkins and John McGinn had scored for the hosts before McGinn struck again for the win.
Dyche said afterwards: "Very frustrating for us. We delivered the first half as I wished they would until the last moment of truth. Credit to them, really good turn and finish. The second goal was a basic mistake and we could have defended better. We scored a very good goal and then gave away another poor goal.
"You can't give basic errors away to teams like this in the Premier League. The mentality is there but you can't keep giving yourself a mountain to climb. Players were switching off to the basics, we have worked on it and shown them but this is the job. I never expected it to be easy when I got here."
On goalkeeper John Victor who went off injured after he was at fault for the third goal, Dyche continued: "I think he is injured and he has hurt himself. He knows it is an error but sometimes it happens. Basic errors are hurting us at the moment. We've got a good group here."
On whether there is a pressure to score goals, he added: "They weren't scoring goals in pre-season and at the start of the season. There is a lot of good in the team but you can't keep giving goals away like this."