Jurgen Klopp admitted that Liverpool had been punished for being wasteful after their 1-0 defeat at home to Manchester United.
The Reds were unable to make their pressure pay off in Sunday's Premier League clash, notably during a first half in which United were constantly on the back foot.
They were kept at bay by United goalkeeper David De Gea before the visitors struck after 78 minutes when Marouane Fellaini headed against the crossbar and Wayne Rooney volleyed in the rebound.
"I didn't see too many chances for Manchester United and we didn't take ours," Klopp told BBC Sport. "Of course it is frustrating. We lost a game that we should not have lost."
The manager acknowledged that Liverpool's familiar inability to deal with balls into the penalty area had also played its part.
"The goal was to defend and we didn't do it," he added. "That is our responsibility. We have to defend set pieces better.
"We did really well creating the chances, but there were a lot of situations where we could have created more chances and didn't.
"There were a lot of things but we lost in a derby against Manchester United so I can't be very positive at this moment so soon after the game."
Klopp went on to tell reporters: "It's really bad: it's a derby and in a derby you only have one job to do; you have to win it. That's the only possibility to be satisfied after the game.
"United at this moment will be happy. You can talk about their performance and it wasn't that good but they won so they are really happy.
"We played better but feel frustrated because there were many things that were good, but our finishing was not good otherwise we would have scored a goal.
"Three mistakes around the goal were too much against a team of the quality of Manchester United. In this moment it is only frustrating, which is how it should be."
Information from the Press Association was used in this report.