Dan Ndoye opened the scoring before Morgan Gibbs-White restored Forest’s lead after Alexander Isak’s equaliser.
Victor Munoz then scored his first Liverpool goal to level the contest. The result puts Forest on the board after their opening-day defeat to Leeds United and extends their unbeaten Anfield run to three seasons.
Glasner felt victory was possible but praised his team’s performance.
“We’re all disappointed because we all feel it could have been more. It could have been a win, but it shows on the other side how well the team performed and how well the players have done,” he told club website.
“Leading twice, creating so many chances, but on the other side we conceded two goals more or less in the same way through the same channel and twice it was the same mistake.
“I could see in this situation that not everything is 100% settled. Of course, here at Anfield you’re getting fatigued, you make a little mistake and you get punished.
“But the reaction was good, after the equaliser we played forward and won the penalty. That’s what I really liked and credit to the players.”