The Reds' title aspirations were called into question on the opening weekend of the season after conceding sloppy goals in their 3-3 draw with Watford, as familiar frailties came to the fore at Vicarage Road.
Liverpool looked far more solid against Palace in their 1-0 win on Saturday afternoon, albeit against a weak attack spearheaded by Christian Benteke, and Klopp believes that his backline deserve more credit.
"We were not 100% happy, but it's not a general problem. We have to work on it," he told reporters. "If you want to start like this, then we defended outstandingly good today.
"I think last week against Huddersfield, Crystal Palace started really football-playing and then Huddersfield were 2-0 up. Then they became a little more direct and using Christian Benteke. I think we really defended this outstandingly good.
"[Ragnar] Klavan and [Joel] Matip did really well in the protection. Joe [Gomez] and Robbo (Andrew Robertson) were really good. You cannot defend it differently, to be honest.
"One problem we had at Watford was we were too early too deep. If you know the other team plays long balls, you have to stay as high as possible as long as possible to create the space for your goalkeeper and use offside."
Liverpool have shipped 27 goals from set pieces since Klopp took charge in October 2015 - only Palace and Watford, both with 28, have fared worse during that time.