Gareth Bale came off the bench to score a remarkable 64th-minute overhead kick that put Madrid 2-1 in front, but the Welshman's second seven minutes from time and Karim Benzema's opener early in the second half were both down to howling mistakes from Karius.
Benzema stuck out a boot to intercept an ill-advised throw from the former Mainz keeper, who fumbled Bale's speculative long-range shot into his net to seal Liverpool's fate.
"The first one, I'm not really sure what happened," Henderson told BT Sport. "The overhead kick, he can do nothing and on the third one the ball has got loads of movement on it. That's never easy.
"It's not about him and the mistakes he might have made. We win as a team and we lose as a team
"It's not about one person, it's about everybody and we just weren't good enough on the night."
Liverpool levelled through Sadio Mane in the 55th minute and the Senegal forward also struck the post at 2-1 – leading the Premier League side's attacking charge after Mohamed Salah departed in the 30th minute with a shoulder injury that could jeopardise his World Cup participation with Egypt.
"It's disappointing, of course. I thought we did well to get the goal and get back in the game," Henderson said.
"But there were mistakes and Madrid are a fantastic side who are always going to hurt you.
"They were the better team on the night but in the first 40 minutes we dominated and had a couple of chances.
"It's frustrating but you've got to give credit to Madrid.
"We did well to get in at half-time at 0-0 [after Salah's injury]. We kept the speed of our game, we got the goal back but there are a couple of goals that on another night wouldn't have gone in."