Immobile tied Gonzalo Higuain's record for most goals in a Serie A season with 36 after scoring in Saturday's 3-1 loss to Napoli.
The 30-year-old Italy forward matched the feat achieved by Higuain in 2015-16, while also collecting the coveted Golden Shoe award for the highest goalscorer in European football.
"I am super happy and proud of what I've achieved, especially when I look back to where I started and everything I went through," Immobile told Lazio Style Channel.
"If you truly believe, sometimes, dreams do come true. I can only thank the coach and staff, my team-mates, and I can assure you these records are for the whole team.
"I also thank the Lazio fans, who made me feel indispensable for this team, and I am so proud of that. I want to be a living example that if you never give up, you can achieve any target.
"I'm so proud to have my place in the history of this sport. I am moved thinking of how my team-mates greeted me in the dressing room after I scored a hat-trick at Verona. That's what the sport is about."
Lazio, who qualified for the Champions League, ended the season in the fourth position, having challenged for the Scudetto prior to the coronavirus-enforced break.