The Sky Living series' biggest ratings to date came on Tuesday, but it still only drew an audience of 105,000 for the channel. It was easily beaten in the Overnights by a Celebrity Who Wants To Be A Millionaire repeat episode on Challenge and a QI repeat on Dave.
Murphy has insisted that he isn't concerned by the figures, pointing out that the numbers for the first episode climbed to 440,000 if they included repeats and catch-up services.
Speaking at the Edinburgh TV Festival last week about the show's ratings, he said: "It was trending on Twitter and Rihanna is the biggest star in the world.
"Find me a channel controller who would turn down Rihanna in her own series."
Styled To Rock is exec-produced by Rihanna and features Girls Aloud star Nicola Roberts and fashion designer Henry Holland as mentors. Cheryl Cole, Scissor Sisters and Katy Perry are among the special guests who have filmed appearances during the series.
Watch Digital Spy's interview with the Styled to Rock mentors: