Aircraft Carrier Vs. Cruise Missile 19

From the Indian Express, during the Malabar Naval Exercises:

ON BOARD USS Kitty Hawk (150 miles west of Port Blair),
September 7: As the small green dots approached closer on the radar screen,
the Indian officer sitting deep inside USS Nimitz knew it was too late to save
the ship. Jaguar maritime fighters of the Indian Air Force (IAF), operating from
the Car Nicobar air base, had managed to come dangerously within striking range
to successfully launch anti-ship missiles on the super carrier.

The IAF registered its first “kill” of the day — none less
than the mighty nuclear powered Nimitz with its compliment of 85 fighters. But
the young officer, on a cross attachment to the US ship, barely had time to feel
proud. The battle had begun in earnest and the target now was India’s lone
aircraft carrier.
INS Viraat, however, proved easy meat for the joint
striking force of US F-18 Super Hornets and IAF Jaguars with the American
fighters deliberately flying over the ship to drive home their air-superiority
skills.

I wonder, with the Army and Marines forced reluctantly to fight a battle of attrition (ie. a sustained conflict) in Iraq, and now winning that battle after much trial and error, if the Navy would be able to fight it's own Iraq if a future war at sea were to last several years?