The Belgium striker has returned to Inter on loan for the new season, moving back to the club he left to re-join Chelsea in a £97.5million deal during the summer of 2021.
Former Everton and Manchester United forward Lukaku failed to hit the heights of previous spells in England, but still finished with 15 goals.
Reflecting on his earlier career at Stamford Bridge, Lukaku said in an interview with DAZN Italia: "I think before, when I left, I wanted to take revenge at Chelsea because when I was young it was my team for 11 years.
"I had the opportunity to go back there and thought I would be a hero, but that wasn't the case.
"In March, I heard there was an opportunity to come back here (to Inter).
"Slowly I didn't say anything, but toward the end of the season we did a very good job with the club and I was able to come back here.
"I make reflections only at the end of the season, so after the last game I put myself to think what my situation was - I saw that as a player with Inter I did well, the season at Chelsea for me was difficult.
"I had no doubts, that is why I made the decision to come back here (to Inter)."
The 29-year-old intends to prove the critics wrong by having an impressive second spell with the Nerazzurri and wants to use the "anger" from an underwhelming campaign at Chelsea.
"The (last) season at Chelsea gave me extra motivation to do even better than before," Lukaku added.
"I think in one year everyone has forgotten about the things I am capable of doing on the pitch. That is a kind of anger that I have inside me.
"That now the [Inter] team has it too, which didn't win last year, all together we hope to do better and bring something home."
Lukaku had a spell at Chelsea as a teenager, but was let go by the club in 2014, eventually joining Everton after successful loan spells with both West Brom and the Toffees.
A £75million move to United followed in 2017, before Lukaku completed another big-money switch to Inter two years later.