"We want to do well in the League Cup and FA Cup but the Champions League spot is the main goal," Lukaku told the BBC.
"It is very realistic when you see the results in the league. The teams that you don't expect to be up there are getting stronger so it is a really exciting time."
Lukaku also thanked former manager Jose Mourinho, who was sacked by Chelsea on Thursday, for allowing the Belgian to join Everton on a permanent deal from Chelsea last year for 28 million pounds following a successful loan spell.
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"I wanted to play and get minutes under my belt. I never got the chance to say it but I would say thank you to Jose Mourinho," said the Belgian international, who has scored seven goals in the last six league games and has 12 for the season.
"I had one conversation with him a few days before I left and I told him I wanted to go and I think he saw in my eyes that I really needed to play because it was the year of the World Cup."
Everton host surprise leaders Leicester City on Saturday.
(Reporting by Shravanth Vijayakumar in Bengaluru; editing by Justin Palmer)
