Home fans turned on the fullback during the draw with Arsenal after he had announced in that week that he would be leaving Liverpool when his contract expires at the end of June.
Klopp, back on Merseyside for tomorrow's Premier League trophy lift at Anfield, was speaking at a LFC Foundation event when Alexander-Arnold's departure was raised.
"I don't want to tell you what you have to think. I can tell you what you think is wrong," Klopp said.
"I don't tell you you should not be angry, you should not be disappointed, I tell you don't forget. This club doesn't forget.
"I watched the game when he came on and I heard the booing. I switched the telly off. Honestly, I could not have been more disappointed at this moment."
The owners must be angry
On working with the Liverpool academy graduate, Klopp was adamant.
"He gave absolutely everything and wears the Liverpool badge in the skin," he said.
'Why didn't he sign a new contract?'. I hear this from fans, this money discussion: 'He goes without a transfer fee'.
"They (the owners) have to be angry.
"This boy, 18 years old, scored a free-kick in Hoffenheim where if he doesn't score that we don't qualify for the Champions League.
"Against Barcelona he did the most cheeky thing in the world and set up the goal for 4-0, a result and a game which will not happen again.
"But now he plays next year for another club and we decide how we deal with that."