Henderson allowed the club's oldest player and Klopp - who'd lost two Champions League finals - to raise the cup in Madrid after a 2-0 win over Tottenham.
“That night was not about me lifting the trophy. I felt me, Millie and the gaffer should have lifted it together," he said.
“It was not about me standing at the front lifting the trophy, it was more about the team. When I look back and see the faces of the lads, that's what means more to me.
“I think everyone looks at the captain to lift the trophy and everyone speaks highly of the captain when you win a competition, but if you rewind to a year or two ago, people would have been criticising the way I am and asking if I should be captain.
“That is not for me to get involved with because they do not really know.
“There is a lot more than the way you play at the weekend. A lot goes into it behind the scenes and that is not just me.
“For me, the photo would have meant the same if the manager was lifting the trophy and I was stood behind him.
“I get just as much from that. It was about the whole night and it was an amazing night just to be involved in."