Henderson paid tribute to Klopp.
"Without this manager this is impossible," he said. "You go through tough times in a season, but what he has done since coming in is unbelievable.
"There's such a togetherness, he has created a special dressing room - all the praise goes to the manager. I'm so proud to be a part of this football club and to cap it with this is so special to me."
The midfielder, who has been at Liverpool since 2011, also captained the Reds in last season's final loss to Real.
"I just try to give my best every time I play football and to help my team no matter what," he said. "I've had tough times but I've kept going - just as this club has.
"It's the best moment of my life. This is what I dreamed of since I was a kid.
"It's not about me, it's not about me being captain or lifting the trophy, it's about this club, these players, this manager. Now we must keep going and kick on."