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.
It is just going to be the beginning of the group stage, and it is always very hard to see a team performing less in their domestic league just because they are preparing for the Champions League. Mostly, these things are done when the Champions League gets tougher, like in the quarterfinal or semifinal stages. This is where most teams bench some of their important players. But in stages like the group stage, where they have more opportunities to play many matches, I don't think any head coach may no try to misbehave early in the their domestic competition by benching players. In fact, Liverpool did not bench any of their key players; they all played. But the truth is that things like this happen in football, where even weak teams will sometimes defeat strong teams.
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.
I don't really think that Liverpool underestimated Nottingham Forest. If Liverpool had underestimated Nottingham Forest, they could have benched their key players, but nothing like that happened. It does happen like this sometimes. In fact, Nottingham Forest has beaten Liverpool before. Even in the last two seasons, Forest was able to defeat Liverpool too. Let's just acknowledge that football is sometimes unpredictable, and we see that every season. It is possible that more unexpected outcomes will happen this season again, where weaker teams may defeat stronger ones.