Howells's comment follow the resignation of BBC director general George Entwistle, who left his post after just 55 days last night (November 10).
Speaking to BBC Radio Wales, Dr Howells called for a number of high-profile BBC staff to resign to help rebuild the integrity of the corporation.
"Chris Patten's been around for a long time. He's a very experienced politician," he began.
"I assume he was appointed because he was seen to be a safe pair of hands. I don't think he has been a safe pair of hands.
"He's probably got to go. Helen Boaden, the director of news, has probably got to go, and a number of other people as well - it's not just George Entwistle.
"Somehow, there has to be a new brush at the BBC."
Howells described the events surrounding the Newsnight crisis - which stemmed from its failure to broadcast an inquiry into child abuse claims relating to the late Jimmy Savile and a second programme that falsely implicated former Conservative party treasurer Lord McAlpine in abuse allegations at a North Wales care home - as the "worst crisis [he could] remember in the history of the BBC".
"Unfortunately, there's a culture at the top of the BBC which is vain, out-of-touch - it's not doing what it should be doing: supporting and encouraging muscular investigative journalism of the highest quality," he said.
"Instead of that, it's all over the place. What the BBC was great at, and why the world trusted it... was because of its journalism. Because of the times it would be uncompromising in searching after truth.
"And now, I don't know what's happened. There's been a real decline in standards, a sloppiness.
"I'm not saying that Newsnight's editors and journalists are not as good as journalists in the past. They almost certainly are - but there's been a problem of management there, a lack of communication between departments, and especially a lack of communication between those vain, great high-and-mighty people at the top of the BBC, and those at the coal-face who are producing the news."
In response to Howells's comments, Patten made it clear that he had no intention of stepping down.
"I think that I now have to make sure that, in the interests of the licence fee payer and the audience, that the BBC has a grip, that we get ourselves back onto the road," he told The Andrew Marr Show.
"I think that my job is to make sure that we learn the lessons of those inquiries and that we restore confidence and trust in the BBC. If I don't do that then I am sure that people will let me know."