Cook scored a total of 23 runs in the two-test series against New Zealand last month as England continued their winless run following their 4-0 defeat in the Ashes.
"My job never changes," Cook told reporters. "It's to score runs at the top of the order. If someone taps me on the shoulder and tells me they don't want me to open for England, it is going to hurt at this precise moment because I want to carry on.
"The hunger and desire is still there but no one has a God-given right to play for England. You have to score the runs to justify your place. Since I've come home I've started to look at my preparation.
"Have I got it right? Do I need to change things? Because that's the right way to do it. I will never sit here and say I've cracked the game or will ever be perfect."
Cook was set to play for first-class county side Essex against Hampshire on Friday in the domestic championship as he fights to make his mark and earn a call-up for England's two-match home test series against Pakistan in May.
(Reporting by Aditi Prakash in Bengaluru; editing by Sudipto Ganguly)
