Oranje played out a 1-1 friendly draw with Belgium on Tuesday, with the Liverpool ace, who had impressed so much in the Nations League win over Germany three days earlier, left on the sidelines.
Koeman believes that will have delighted Klopp, who has taken issue with UEFA over the introduction of the Nations League in an already packed fixture calendar.
Speaking last week, the Reds boss, who branded the competition "senseless", said: “You have to call the manager of any country and say: ‘Can you leave players out?’ and he says: ‘I am under pressure as well.’”
Koeman, who saw Virgil van Dijk return to Anfield prematurely, joked to Sky Sports in response: “Maybe Mr Klopp is now very happy, and that's okay. I hope I am back in the good books!”
After missing out on Russia 2018 in the summer, Koeman has successfully stabilised what was once an ailing Netherlands side, and though he is pleased with the progress that has been made, he is aware there is still much to be done.
“We know it is long way back, but we have seen a real improvement in the team. We started against Germany and got a really good win against a big opponent,” he said.
“It is all about the final result. If you play France away, and don't have that final result then it is always difficult. One way to improve is to show what we can do and play good football, but the most important is to have a good result.
“We beat Portugal, we lost 2-1 to France, we played Belgium and drew 1-1, we won against Germany and we got a draw away against Italy - these are not the easiest of matches. We are in a good way and I am really proud of the team.
While the Netherlands are no in action until next month, when they will face France and Germany in their final two Nations League matches, Liverpool are back in action on Saturday, when they travel to Huddersfield in Premier League action.