Readers of The Daily Telegraph newspaper recently claimed that scenes in the October 24 episode bore a startling resemblance to parts of the novel Little Women and the 1942 film Mrs Minerva.
One viewer described the episode as having "the finest example of coincidence I have ever heard and seen".
The claims also follow criticisms of the series in the media, which prompted Fellowes to hit out at what he describes as a "permanent negative slant" towards the show.
Speaking to the The Independent on Sunday, the Oscar-winning screenwriter said: "All we get is this permanent negative nit-picking from the left. You just want to say relax!
"It's a show that might not appeal to the left. I mean, why is it that it's The Independent on Sunday ringing me up about this? There are plenty of shows on television I don't like but I don't go on about them."
However, Fellowes admitted that he had read Little Women and seen Mrs Minerva, meaning some of the scenes could have stuck in his mind.
"Who can say what is lodged in one's brain?," he said. "I am not conscious of lifting either, but it doesn't mean [the viewers] are wrong."
Since its premiere in September, Downton Abbey has proved a major hit for ITV on Sunday nights, with the latest episode attracting more than 9 million viewers. The broadcaster has already commissioned a second series.
Despite the success, Fellowes confessed to being left "depressed" by the criticism, which includes accusations of a string of historical inaccuracies, such as a TV aerial being shown on a house.
Lashing out at the critics, he said: "The real problem is with people who are insecure socially, and they think to show how smart they are by picking holes in the programme to promote their own poshness and to show that their knowledge is greater than your knowledge."