Lukaku was a key figure in Saturday's (AEST) UEFA is Europa League showpiece against Sevilla, opening the scoring early on from the penalty spot after being hauled down by Diego Carlos, who controversially avoided a red card.
Sevilla battled back and a brace from Luuk de Jong put the Spaniards on top before Diego Godin restored parity.
Lukaku might have put Inter back in front in the second half but was denied with only Yassine Bounou to beat.
He then diverted Diego Carlos' overhead-kick into his own net 16 minutes from time as Sevilla went on to lift the trophy for a sixth time in 14 years.
On Sunday, Lukaku posted to his Instagram account for the first time since that loss as he promised the situation would motivate him.
First of all i want to say thank you for all what you guys have done for my family and myself. This year as a team we grown a lot together and it’s an honour to represent a club that i loved since i’ve been a kid. Yes what happened in the final pissed me off but i will fight back. I never had shit the easy way in life as many of you know and this experience will make me stronger. 1 thing is for sure inter is not dead and this experience will make us better as a team! there’s unity and we’re heading the right direction. To the fans i want to say thank you for being so supportive every game home or away i love you guys. I appreciate the messages i’ve got. We will be back sempre forza inter 🖤💙
"First of all, I want to say thank you for all you guys [Inter team-mates] have done for my family and myself," he wrote.
"This year as a team we've grown a lot together and it's an honour to represent a club that I loved since I was a kid.
"Yes, what happened in the final p***** me off but I will fight back. I never had s*** the easy way in life, as many of you know, and this experience will make me stronger.
"One thing is for sure, Inter is not dead and this experience will make us better as a team! There's unity and we're heading in the right direction.
"To the fans, I want to say thank you for being so supportive every game, home or away. I love you guys. I appreciate the messages I've got. We will be back."
Despite Europa League final disappointment, Inter will be in the Champions League next season after it finished second in Serie A.
However, the future of head coach Antonio Conte is in doubt after he hinted at the end of Satruday's match that he may not be in charge next season.