Both the films have been recognised in the best picture category besides cold war-set "Bridge of Spies", period romance "Brooklyn", action thriller "Mad Max: Fury Road", space adventure "The Martian", captivity drama "Room", recession drama "Big Short" and news drama "Spotlight".
"The Martian" has bagged seven nominations while "Carol" and "Spotlight" got six each. The nominations were announced today.
Apart from the best picture, best actor for DiCaprio and best director for Inarritu, the movie has bagged nominations for best supporting actor (Tom Hardy), best cinematography, sound editing, costume design, sound mixing, film editing, production design, visual effects and make up and styling.
DiCaprio will fight it out with last year's best actor winner Eddie Redmayne (The Danish Girl), Michael Fassbender for "Steve Jobs", fellow Golden Globe winner Matt Damon "The Martian" and Bryan Cranston for "Trumbo".
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Miller ('Mad Max: Fury Road'), Tom McCarthy ('Spotlight'), Adam McKay for "The Big Short" and Lenny Abrahamson for "Room".
Besides Hardy, the best supporting actor award nominees are this year's Golden Globe winner Sylvester Stallone ('Creed'), Mark Rylance for "Bridge of Spies", Mark Ruffalo for "Spotlight" and Christian Bale ('The Big Short').
The best supporting actress honour contenders are Rooney Mara ('Carol'), Jennifer Jason Leigh for "The Hateful Eight", Alicia Vikander ('The Danish Girl'), Kate Winslet ('Steve Jobs') and Rachel McAdams for "Spotlight".
Indo-American filmmaker Sanjay Patel's "Sanjay's Super Team" is nominated in the best animated short film category. Also contending for the award in this category are "Bear Story", "World of Tomorrow", "Prologue" and "We Can't Live Without Cosmos".
It will see competition from "What Happened, Miss Simone?", "The Look of Silence", "Cartel Land", "Winter on Fire: Ukraine's Fight for Freedom".
24th James Bond "Spectre" has been ignored by the Academy apart from the lone nomination in the original song category for Sam Smith's "Writing's on the Wall".
The track will face stiff competition from "Earned It" (Fifty Shades of Grey), "Simple Song 3" from "Youth", "Manta Ray" from "Racing Extinction" and "The Hunting Ground" number "Til it Happens to You".
The nominees for original screenplay are Tom McCarthy and Josh Singer for "Spotlight", Matt Charman, Joel Coen and Ethan Coen for "Bridge of Spies", "Ex Machina" director-writer Alex Garland, Jonathan Herman and Andrea Berloff for "Straight Outta Compton" and "Inside Out" scribes Pete Docter, Meg LeFauve and Josh Cooley.
The adapted screenplay category will see "The Big Short" screenplay by Charles Randolph and Adam McKay, "Brooklyn" by Nick Hornby, "Carol" by Phyllis Nagy, Drew Goddard's screenplay for "The Martian" and author Emma Donoghue's adaptation of her novel for "Room".
The comedy-drama "Inside Out" leads the best animated feature film category, with another nomination in the best original screenplay.
"When Marnie Was There", "Anomalisa", "Boy and the World" and "Shaun the Sheep Movie" are the other nominees for best animated feature film category.
The 88th Academy Awards will be presented at the Dolby Theatre at Hollywood & Highland Center on February 28.