Taiwo Awoniyi's winner stunned the visitors as Forest climbed off the bottom of the Premier League with a 1-0 victory.
The striker never played for Liverpool in six years at Anfield and was loaned out seven times before joining Union Berlin last year.
Liverpool remain seventh having failed to build on last week's 1-0 win over Manchester City and are yet to win away in the league this season.
"Who can be blamed for not finishing the situations off? There are not a lot of people out there, it's just us," said Klopp, who was without Thiago after he woke up with an ear infection.
"That's why you have to feel it. It's a big blow for us because we wanted to get the three points," he added.