Wolfsburg came from behind to triumph in Thursday's round of 16 first leg with Carrizo arguably at fault for all three of the home team's goals.
Carrizo got his hands to Naldo's first-half equaliser, which cancelled out Rodrigo Palacio's fifth minute opener, but could not parry the powerful header, while the Argentinean keeper gave away possession in the 63rd minute, allowing Vieirinha to tee-up Kevin De Bruyne.
De Bruyne added a third goal with 15 minutes remaining, curling a free-kick beyond Carrizo's left hand on the side of the goal not defended by the wall.
But at his post-match media conference, Mancini insisted each goal could have been avoided if Inter had maintained possession and not given the ball away to Wolfsburg.
"Why did I play him [Carrizo]? He always played well. I don't think it's his fault if we lost 3-1," the former Manchester City manager said.
"That was a mistake [on the second goal] anyone can make...
"You want to recall that set piece [De Bruyne's second goal]? Well, we had the ball but my players weren't able to play it. That's why I blame them for it. They are capable of playing, therefore they have to manage and control the ball, and not just to waste it like that, leaving it all to chance.
"You give away a set piece and from that a goal can happen. Kevin De Bruyne is not the sole factor. Carrizo may have made a mistake but earlier in the game he had made a couple of great saves."
But speaking to Inter's website after the match, Carrizo conceded he was at fault for the goal that put Wolfsburg ahead.
"I made a mistake and I'm obviously not happy about it because up until that point we were playing well," he said.
"I think we have reason to be confident though, given that they only took the lead because of an individual mistake.
"It was my fault tonight but I'm not going to let it get to me. I feel I have everyone's backing."
