Lukaku has never hidden from the fact that he wants Champions League football - an aspiration also held by Blues boss Roberto Martinez - and he believes that Everton’s quartet of stand-out young players will be ready to mount a more sustained challenge next season.
"Stones is just going through a phase"
“Champions League is really important,” said Lukaku, speaking at Longmoor Community Primary School earlier this week in his role as Everton’s Kick It Out Next 20 ambassador.
“At the end of the day you just want to perform.
“Why do you get praise? Because you perform well.
“It is easier to put a 21-year-old out of the team than a 32-year-old so you need to keep working and keep progressing.
“That is my personal challenge, to keep progressing and keep working.
“Ross gets it as well now and Stonesy is going through a period that he has never had in his career.
Everton's Romelu Lukaku, Ross Barkley and John Stones
“He is going through a period now because he knows Funes Mori is knocking on the door and Jags is doing great.
“That is when you know it is a mental aspect now that has to come up.”
He added: “If you look forward and down the line, then Champions League is the objective of the club with us.
“You have Geri, myself, Ross, Stonesy. We are the four but you have to deliver more wins, get that nastiness inside of us but you don’t get that straight away, but with age.
"The Champions League is the objective for ALL of us"
“So if you talk about next season then you can say that those boys are ready.
“Now, to be fair, this is Ross’ best season in the Prem, it is Stonesy’s best season in the Prem so people expect from him, it is Geri’s best season in the Prem and this is my best season in the Prem as well.
Lukaku converts the penalty to scores his team's first goal during the 3-0 win over Stoke City at Britannia Stadium on February 6
“I’ve scored as many goals as last season but we are only halfway.
“But because I’m a striker, nothing has changed, it is always the same drill but it is different for them because they play in a different position.
“I have been in the game for six or seven years now, so I know how it is. This is nothing new, I know the expectations from people but then, for them, how are people going to judge is when they have to realise ‘I have been in this situation before and nothing is going to stop me’ and next year the team is going to much stronger than it has been this season.”