Callum Hudson-Odoi came off the bench to score the only goal of the match and bolster the squad's unbeaten record in the league so far this year, at two wins and two draws.
"Very happy. Many of our fans today in the stadium, they were not even born (in 1969). So that says how hard it is to play here," Espirito Santo told reporters.
"Proud of the way we played as a team ... it's all about taking your chances in the right moment and we did it."
Forest were without their two starting midfielders, after Danilo broke his ankle last month against Bournemouth and Ibrahim Sangare was taken out by a hamstring injury.
Centre-back Willy Boly was also absent with a calf injury.
"Unfortunately, Ibrahim Sangare is going to be a while," Espirito Santo said. "I wish we could have everybody ready. Unfortunately we don't have three players with us ... we have to be ready for everything."
Forest also played central midfielders Nicolas Dominguez and Elliot Anderson as wingers to track Liverpool's full-backs, he said.
"It is about building and believing in this idea that you can develop," he added.
Forest, who finished 17th last season, will visit Brighton next Sunday.
