The 3-0 to reverse to the Serie A club at a sold out Murrayfield in Edinburgh made it four winless friendlies in a row for a Reds side missing several vital pieces.
Mohamed Salah, Sadio Mane, Roberto Firmino and Alisson are all missing because of extended holidays after international commitments. Xherdan Shaqiri and Naby Keita have been absent through injury.
The German coach admitted that being without those players had caused problems for pre-season but did find a silver lining.
“Finally, this period is over,” the 52-year-old told LFCTV after the game.
“I never had a preseason like this, without six players missing a complete pre-season. It’s just strange.
“Tomorrow a couple of them come back, it would be better if they had come earlier, but that’s how it is.
“The best news is [Manchester] City have no idea who they face next week because we will surprise ourselves probably!”
Klopp’s side face City in the Community Shield at Wembley on August 4.
The traditional curtain-raiser to the English season will be a chance for the Merseyside club to make a statement against the side that beat them to the Premier League title by one point last season.
They are expected to welcome back five of the six absentees this week, with only Mane, who helped guide Senegal to the final of the Africa Cup of Nations, remaining away from the group.
“Shaqiri and Keita as well, they trained already with us once, one session. They will come tomorrow and they should be a step further," Klopp said.
“We will see, hopefully they can play a couple of minutes on Wednesday. Five of six back, which is good.”
After the Community Shield, Liverpool open the Premier League season with a game against newly promoted Norwich City on August 9.