The original "The Pigtail" was a romantic and sentimental poem about the love a man feels for a young woman with beautiful pigtails. Thackeray's parody likely mocked the poem's sentimentality, romanticism, and possibly even its subject matter.
Unfortunately, Thackeray's "Pigtail" is lost to history. There are no surviving copies, and only a brief mention in Thackeray's letters confirms its existence. We can only speculate on its contents, but given Thackeray's satirical nature, it was likely a humorous and biting critique of the original poem.