Murillo, Nicolo Savona and Morgan Gibbs-White scored for Forest, who were languishing in the drop zone before kick-off, to inflict Liverpool's sixth defeat in their last seven league games.
"Another big disappointment," Slot told reporters. "We started off quite well for the first half an hour. We conceded the 1-0, and we weren’t able to play the way we did in the first half hour."
The Dutchman conceded his tactical tweaks failed to spark a response.
"If things go well or things go bad, it’s my responsibility. We weren’t able to create enough. I tried to adjust a few things, but it didn’t work out. We were unable to score a goal," the Dutchman said.
Forest's Savona scored inside the first minute of a second-half collapse by the home side.
"Of course, it was damaging. It was already hard to be 1-0 against a team blocking everything," said Slot, who was serenaded by visiting fans singing "You're getting sacked in the morning".
Liverpool have lost eight games in last 11
Liverpool have now lost eight of their last 11 games in all competitions.
"In a few days, we have to play in the Champions League again (Wednesday when they host PSV Eindhoven), and then play three Premier League games in a short space. Keep your head up and work incredibly hard. We are trying every single day," Slot said.
The manager admitted experience alone will not solve the problems.
"It’s always helpful to have experienced and quality players," he said. "It’s not working out at this moment."
Injuries have played their part, with Florian Wirtz and Conor Bradley the latest casualties, and summer big-money signings such as Alexander Isak have yet to settle.
Isak, the most expensive player in league history, started but was largely unnoticeable and Slot replaced him midway through the second half.