The 49-year-old Jeev said Father's Day on Sunday was "another sad reminder of what I've lost".
"Dad was much more than my father - he was my best friend, my guide, my mentor," Jeev, who was in Dubai when Milkha tested positive for COVID-19 and reached here in a couple of days to be with him, said in a tweet.
"I hope I've the same resilience & inner strength to overcome all odds. I really need it now. And I will need it for the rest of my life," he added.
Milkha was cremated here on Saturday evening with full state honours with Jeev lighting the pyre. Milkha also had three daughters.
Sports Minister Kiren Rijiju, Punjab Governor and Chandigarh Administrator VP Singh Badnore, Punjab Finance Minister Manpreet Singh Badal and Haryana's Sports Minister Sandeep Singh were among the dignitaries who attended the last rites.
The family's tragedy was compounded by the loss of Milkha's wife and former national volleyball captain Nirmal Kaur just five days before the legendary sprinter's death. Nirmal had also been battling COVID-19.
"Somehow, I don't remember much of Dad's funeral procession, but one sight I will never forget. A military van coming to a stop and these soldiers getting out and giving dad the salute.
"The Milkha family has always been grateful of the Indian Army, and I want to thank them again," said Jeev.