Francesco Acerbi and Marcus Thuram scored in each half to secure Inter's 20th Serie A title and a sixth consecutive win against Milan, who scored a late goal through Fikayo Tomori.
Martinez, the top scorer in Serie A with 23 goals, celebrated his first Scudetto victory as Inter captain having also won the title in 2021.
"Now, I feel like crying because we worked so hard, suffered so much, we deserved this joy. I dedicate it to my family in Argentina, my children, my teammates and all the fans," the 26-year-old told DAZN.
"I told the lads, we were in a situation that had never happened before, we had to make the most of this opportunity to win in a Rossoneri stadium."
The Argentina international said he is keen to remain at Inter though they have yet to conclude an extension to his current deal, which expires in June 2026.
"I hope so (to renew), we need to reach an agreement with the club," Martinez said.
Inter CEO Giuseppe Marotta told Sky Italia they were in talks over a new five-year contract with the forward.
"(There will be no problems with renewal), absolute loyalty after winning his seventh trophy with Inter," he added.
