Lukaku expressed his European ambitions last week, casting doubt on his Toffees loyalty as the club is unlikely to qualify for the UEFA showpiece this campaign.
The Belgian - who has hit 25 goals in all competitions in 2015/16 - has recently been linked with numerous continental giants, including Juventus, Paris Saint-Germain, Real Madrid, Bayern Munich and Manchester United.
"It [Lukaku's comments] is not unsettling at all because that should be the aspiration of everyone, wanting to be as good as you can and trying to aspire to reach the best competitions," Martinez said.
"At Everton we've got that aspiration. We want to be in the Champions League, I've said it openly for a long time.
"We want to be competing to win titles. We've just been in the semi-finals of the League Cup and marginally we got knocked out against the eventual winners [Manchester City].
"Now we are in another semi-final of the FA Cup. We want to be in those sorts of situations. We want to create a real good, positive momentum and the players need to be part of that."
"But clearly we're relying on the performances of the players. We need ambitious players and we need players who can carry the expectations of our football club."
The Spaniard added: "We shouldn't be afraid about losing players because we are in a position where financially we can compete against anyone in world football at this present time. Things have changed radically in that respect.
"It's not about talking about an issue, it's the example of the last six windows that we've had. All we're doing is, from window to window, becoming stronger and making a more talented squad, putting together a group of players that can take us to where we want to get. And that's what we're going to carry on doing.
"But at the moment it's the wrong time and pointless to talk about individual situations."