I thought it would be best to break the statement down into its constituent parts.
"I regret that one email was quoted incorrectly ..."
If you didn't know the backstory here you would think Karl was referring to some sort of editing error. What seems to have happened is that a Republican source gave him what they said was a direct quote from an email but which turned out to be inaccurate. The fact that it was wrong in a way that appeared damaging to the White House (the opponents of the Republican sources in this case) suggests it may not have been an innocent mistake. But whether they were playing games or just sloppy is secondary to the fact that the quote was wrong.
"... and I regret that it's become a distraction from the story, which still entirely stands."
This is simply false. Folks on either side can disagree over how much it changed the story. But you can't have a major part of the story be false and have the story 'entirely stand'. Here Karl is doubling down on his original claim that the fact that his quotes were wrong didn't change the story. Not so. A central point of his story was White House involvement and White House involvement on behalf of the State Department. The alleged quotes were key evidence for that claim but the quotes were wrong. Ergo, the story cannot 'entirely stand.' Calling this error a 'distraction' from the story is incorrect because the error undermines the story itself.
Indeed, even within the normally collegial norms of elite reporters, CNN's Jake Tapper and CBS's Major Garrett have both said the bogus quotes change the story significantly or undermine it entirely.
"I should have been clearer about the attribution."
Here's where you see that this very short statement is like a tightly-bound set of interlocking misdirections. Karl repeatedly said that he reviewed the actual emails. But he didn't. And that's not a minor point because the impact of his story was based on his having reviewed them himself rather than relying on a second hand account -- having gotten some summary of them from a tendentious source -- a Republican staffer. The fact that Karl put the non-quotes within quotation marks makes it pretty clear that he was led to believe that he was being given verbatim transcriptions. You never put summaries in quotes.
To see what difference this makes, imagine rewriting the article as "I've reviewed notes taken by a source who was allowed to read but not make copies of the emails ..." If he'd written it that way, the credibility of his source would have immediately become central to the story -- and since investigators or Hill staffers are the kind of people who get allowed to review but not make copies of documents it would have been fairly clear that he'd gotten them from Republican staffers.
(We seem to know definitely that the sources were Republicans since CBS's Major Garrett said that. He must know either because Karl told him or because Garrett too was offered the same notes from the same source.)
Again, see how the parts interlock: Falsely claiming to have reviewed the actual emails made the source's credibility irrelevant since Karl had seen the actual emails. Had Karl not said that, this all would have been on the source who passed him inaccurate quotes. Had the quotes been accurate, none of this would have surfaced. The fact that they were inaccurate made Karl's claim untenable.
"We updated our story immediately when new information became available."
One of the most comical parts of the Dan Rather/Bush National Guard records fiasco came when Rather tried to shift gears after it was finally definitively clear that the records were bogus. Rather did one segment after this became clear where he basically said, 'Yep, the fact that these were forgeries is a dramatic new turn in the story. And we're on it!' Note the single quotes; I'm paraphrasing.
When your story ends up being based on bogus information, that's not a new development in the story. It means your story was wrong. And you need to say you made a mistake.
Here's a better way Karl could have addressed the problem. "I regret that quotes contained in my original article turned out to be wrong. I also should have been more clear that I'd been given notes taken by someone who'd read the emails rather than the emails themselves. I regret the error and we've revised the article in light of the new information."