The on-loan forward believes there is nothing preventing the Toffees aiming for Europe's elite competition after starring in Saturday's Merseyside derby
The Belgian scored his sixth and seventh Premier League goals of the season in his first Merseyside derby as Everton looked to be on their way to a long-awaited victory over their local rivals, although a late equaliser ensured the points were shared.
"To play in the derby was such an honour and to two score two goals," Lukaku told BT Sport. "My team-mates helped me a lot. To help the team get back in the game, it was great. The pity was that we didn't win.
"It [Lukaku's second goal] was a great header. We worked a lot of set pieces, but it usually doesn't come off. Week after week I just try to improve. Every game in the Premier League is a big challenge.
"This year we have a great squad, a lot of experience and a lot of young players too. It's a good mix. Hopefully we'll end up very high in the league. Champions League - why not?"
Meanwhile, Toffees manager Roberto Martinez lamented his side's set-piece frailties after a late Daniel Sturridge header denied them the three points.
The hosts were denied a first Merseyside derby win since October 2010 thanks to Sturridge's conversion of a Steven Gerrard free-kick a minute from time at Goodison Park. Philippe Coutinho had previously opened the scoring following a Liverpool corner.
"The two teams played in the right manner, created a lot of chances," he said.
"But conceding two goals from set pieces is very disappointing. We were [trailing twice] when Liverpool didn't even have a shot on target [from open play].
"Overall I think we had the better chances, I think Liverpool got too big a reward from the game. But overall it was a fantastic football game."