Firstly, I must say that I do not agree with the notion that Douglass uses "emotional manipulation" to convince his readers of the obvious evils of slavery. "Persuasion" would have been a better word for your instructor to use.
That said, sentimentalism was a very common rhetorical strategy during the nineteenth century, used by Harriet Beecher Stowe in Uncle Tom's Cabin and later, by Douglass, in his short story "The Heroic Slave," a fictional rendering of the story of the slave insurrection led by Madison Washington on-board the Creole.
In his autobiography, to which I assume you are referring, you could argue that Douglass uses sentimentalism to talk about his departure from Colonel Lloyd's plantation. He finishes Chapter V by acknowledging the reader's suspicion that he might be "superstitious" and "even egotistical" for believing that God intervened in his favor, so that he would be chosen among all of the other children on the plantation to leave. In fact, he says that he "should be false to the earliest sentiments of [his] soul, if [he] suppressed the opinion."
Sentimentalism, according to Merriam-Webster's Dictionary, is the quality or state of being defined by feeling, sensibility, or emotional idealism. The philosophy of moral sentimentalism, which may have guided abolitionist principles, is to use feeling and sensibility to guide conduct. However, what Douglass seeks is not simply feeling from the reader, but feeling as a guide toward empathy. For this reason, it is not manipulation, word which suggest malicious intent or exploitation, but persuasion that he employs, which helps people who are otherwise very distant from the problem of slavery to understand how it feels to be owned, to be abused, to be starved, to go without clothes in winter, all of which Douglass describes. By narrating his relief about being sold to the Aulds, he helps the reader feel what it is like to be rescued, in a sense, as well as to understand his faith in God. Very often, in sentimental writing, the narrator directly addresses the reader. Douglass does this in the passage at the end of Chapter V.
In another instance, in Chapter VII, he talks about the impact of literature on his understanding of his condition. He mentions "The Columbian Orator," a book edited by Caleb Bingham (not to be confused with the painter George Caleb Bingham) that was used to teach children public speaking. In it was a dialogue between a master and a slave. He also discovered Irish dramatist Richard Sheridan's speeches on behalf of Catholic emancipation.
Reading gave him perspective but, as his master had predicted, it also "[torments] and [stings his] soul to unutterable anguish." Thinking became his torment and his knowledge and analytical ability became inextricable from his senses. He heard freedom "in every sound" and saw it "in every thing":
I saw nothing without seeing it, I heard nothing without hearing it, and felt nothing without feeling it. It looked from every star, it smiled in every calm, breathed in every wind, and moved in every storm.
Here, he is employing the sensibility common to sentimental literature, as well as the use of nature as a motif. Douglass also draws a connection between freedom and nature to suggest that freedom is natural, while the state of bondage is unnatural.