The Reds triumphed 6-5 on penalties after the game ended 0-0 after 120 minutes at Wembley Stadium.
“That we won now both domestic cups, that really is special,” Klopp told reporters.
“That Trent Alexander-Arnold is the youngest player ever in this incredible history of the Premier League who won all six major trophies, at 23, the youngest. So many special stories.
“After the game I said to Thiago, if I would have known what a player you are, I would have signed you four years earlier.
“He said, ‘You taught me running!’ I take that, it’s fine. He could obviously already play football pretty well but he learned running in Liverpool, that’s fine.”
Klopp refused to be drawn on his side’s Premier League prospects, nor their European ambitions ahead of the final against Real Madrid, instead preferring to enjoy the moment.
“For tonight I decided to take that and just enjoy this moment and don’t think about the next challenge we are facing. Because it’s really special, it’s really special,” he said.