Bloom's musical sitcom has previously scored three Emmy nominations, but this year has missed out in what's a very competitive field among both the drama and comedy categories.
Bloom also today posted a timely clip from Crazy Ex-Girlfriend, a musical number titled I Don't Care About Award Shows.
Elsewhere in today's Emmy nominations, former Grey's Anatomy star Sandra Oh, who scored rave reviews for her star turn in this year's Killing Eve, made Emmys history by becoming the first woman of Asian descent to be nominated for Lead Actress in a Drama Series.
Chef and presenter Anthony Bourdain, who died last month aged 61, has received several posthumous Emmy nominations.
Bourdain's CNN series, Anthony Bourdain: Parts Unknown scored six nominations, while a
seventh went to his Explore Parts Unknown on cnn.com.
The 70th Emmy Awards will be held in Los Angeles on September 17.