Maybe one of the reasons for Liverpool's defeat is that they wanted to prepare for the Champions League match. The Champions League is more important and Nottingham was an opponent they did not see as strong.
What I know is that Liverpool underestimated Nottingham, and Nottingham Forest surprised everyone in the match. I don’t think the Champions League match was the reason why Liverpool's attention shifted from the Nottingham Forest match, and are you even saying Liverpool can’t participate in both the Premier League and the Champions League at the same time? I don’t see any reason why Liverpool should take their Champions League match seriously over the Premier League, seriously, the result of Liverpool vs. Nottingham Forest was just a surprising one to me.
They must have thought that they could beat them in any way and underestimated them. But you shouldn't do that. You should take every opponent seriously, both in the league and in the Champions League. This defeat could even cost Liverpool the championship at the end of the year.
At least they will have learned their lesson that no opponent should be underestimated, no matter how poor the opponent’s performance is. Always make use of your main squad to start every match, and after winning comfortably, most of those players can be substituted so that they will be able to rest.