Over 40 fans were injured as a car drove into the crowd as people celebrated Liverpool's Premier League title triumph.
Klopp attended the parade on Monday, having returned to Merseyside for Sunday's Premier League trophy ceremony.
He posted to social media: "My family and I are shocked and devastated, our thoughts and prayers are with all those who are injured and affected.
"You'll never walk alone."
Meanwhile, Reds legend Sir Kenny Dalglish also posted: "Shocked, horrified and deeply saddened about what happened at the end of the parade today.
"Our thoughts and prayers go out to everyone and their families who have been impacted by today’s tragic event. Our anthem has never felt more appropriate, You’ll Never Walk Alone. Your Liverpool family are behind you."