Scrum-half Brendon Leonard, who scored the winning try in Cardiff, dotted down after just two minutes and Giulio Toniolatti added a try of his own.
Zebre may have been made to regret a host of missed penalties but the Blues could only manage one converted try, through Tom Williams, and a Gareth Davies penalty.
McIntosh conceded errors had played a large role, but he was adamant the Blues players had not let themselves down with a lack of effort.
"We gave away some silly penalties and a couple of organisational errors in defence by certain individuals cost us two tries," he said.
"We've got to reflect on the negatives to make sure that we put them right.
"There was no lack of effort. We are pretty harsh taskmasters and we will name and shame when we need to. But it's not a case of that today.
"I thought the boys were admirable in their attempt but a few decisions just didn't go our way which meant we have come second."
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