Carver was taken down by Worcestershire’s Ross Whiteley towards the end of the T20 match at Headingley, but Bresnan accepted personal responsibility.
“It was probably a captaincy error on my part,” he said.
“Did Karl have to bowl at that time? Maybe not. But I rolled the dice when maybe I didn’t have to.
“At the end of the day, we still came out with a win, and I think I’ll learn a lot from that and Karl will learn a lot from it.
“It won’t affect him because he’s mentally strong, and these things can happen in Twenty20.”
Bresnan’s comments were echoed by first team coach Andrew Gale, who said: “I’ll blame Bressie because it was poor captaincy there bowling him at that stage of the game.
“Bowling to Ross Whiteley, with the short boundary, poor Karl’s gone for six sixes and you’ve got to feel sorry for him.
“His first over was really good, and he’s got a really good record in Twenty20 and one-dayers. He’s never let anyone down, Karl, and he’ll bounce back.”
Although on the wrong end of history, Bresnan and Gale presided over another excellent display by Yorkshire, who have now won three of their six group games to go top of the North Group.
David Willey hit a career-best 118 out of their 233-6 yesterday, Worcestershire replying with 196-7.
“The team is going out and playing exactly how we want,” said Bresnan, “and I take my hat off to Dave Willey; it was incredible striking.
“It doesn’t matter who bowls at him; he just fancies a piece of them, and that’s a great attitude to have in this form of the game,” he said.
“Everybody is chipping in, and I thought Steve Patterson bowled outstandingly well at the death, conceding just eight runs from his three overs.
Gale agreed: “I thought it was an outstanding performance to cap a really strong week.
“Now we’ve got to keep it going in our next home game against Durham on Wednesday.”