The Belgian netted a late double as his side thrashed Shakhtar Donetsk to set up a final date with Sevilla as they look to win their first silverware since 2011.
But while Lukaku says that "records are there to be broken", his main focus is bringing success to the trophy-starved San Siro club.
"At the minute everything is going well but we keep fighting," he told BT Sport after the match.
"Records are there to be broken but we want to win. We need to prepare ourselves really well, recover and play again.
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"The team is doing well and everybody is doing their best. We worked really hard in the camp. It's tough but you see the results of the hard work. We want to keep going.
"We knew they were really good in combinations so as long as we kept the centre of defence close, we knew we would not have problems as the physicality of us is too much for them."
Lukaku moved to Inter from Manchester United last summer and is pleased to see his former side making progress after reaching the Europa League last four themselves.
"Man United tried their hardest. They had a good season and Ole [Gunnar Solksjaer] did a good job," he added.
"Mason Greenwood is coming through and Marcus Rashford. I am really happy for them. They look good for next season so I have no doubts."
Coach Antonio Conte said that he was determined to bring silverware back to San Siro and admitted that his side were somewhat in the shadow of the treble-winning side of 2010.
"It's difficult to forget the treble. That Inter was a fantastic team and they won the treble, now after 10 years we have the chance to lift a trophy.
"It's a great satisfaction to me and my players. We want to give satisfaction to our fans. But we have to deserve to lift the trophy. We have to play against a strong team.
"Sevilla have great experience in this competition, we have a lot of players who are playing in this competition for the first time. At the same time, we have enthusiasm, we have strength, we want to give satisfaction to our fans and we'll try to do this."
Conte also hailed his side after playing a "perfect" game in the semi-final, saying it was a testament to their hard work in training.
"We played a perfect game, we prepared the game very well. We knew Shakhtar were very good in possession.
"We pressed them very high, we took the risk but at the same time they played with great patience. I'm very happy, very happy for my players because when you work very hard and stay every day to prepare for games with video analysis, tactical sessions every day and have this type of answer from my players is fantastic for me."
Inter Milan and Sevilla meet in the final on Friday.