Mohamed Salah fired the home side ahead in the 17th minute, but their lead lasted just 10 minutes before Ajax pulled level with a stunning strike from Mohammed Kudus.
Liverpool, beaten 4-1 at Napoli in their group opener, looked to be heading for another disappointing result until centre-back Joel Matip scored in the 89th minute.
"You do a lot of good stuff, we played a really good game...And then you concede, you are 1-0 up and you concede with the first chance of the opponent, the equaliser," Klopp told reporters.
"So, that's what I mean, it's typical, like a proper setback."
Klopp praised Liverpool's reaction to the "incredible" leveller from Ajax.
"I was not surprised when they scored, not because we defended badly but because it's pretty likely in situations like this," he added.
"Pretty much every other shot (Alisson) would have saved, but this one was one you couldn't save. The reaction to show that we are still able to show these kind of things was the most important thing tonight."
