The Gunners reached the Europa League final last term but were crushed 4-1 by Chelsea in Baku.
Boss Unai Emery is plotting a summer overhaul of his squad after Arsenal fell away at the end of last season to miss out on a top-four place.
Defensive reinforcements and a winger in the form of either Wilfried Zaha, Lucas Vazquez or Ryan Fraser are the manager’s priority.
But as yet only one deal has been completed, a £5m swoop for 18-year-old attacker Gabriel Martinelli.
And it seems Lacazette is trying to dampen expectations before the new campaign gets underway.
The France international told FourFourTwo: “A club like Arsenal has to be playing in the Champions League every season.
“We will start to think about winning the biggest titles in a few seasons.
But first we need to make sure we are in the Champions League consistently again.”
But some Gunners fans were left confused by the comments, questioning why Arsenal shouldn’t be able to target the biggest trophies immediately.
“We haven’t won a league for 15 years ffs. The fans have waited too long already Mr Lacazette,” tweeted one Gooner.
A second wrote: “What? Pre-season hasn’t even started yet…..hmmm. I will still not give up on Arsenal.”
Another fired shots at Lacazette’s efforts, adding: “He ain’t gonna contribute to that getting 11 goals a season…”
Pierre-Emerick Aubameyang agreed with his strike partner, stating that top-four is a must.
“That has to be the main target of every Arsenal season,” he added. “You come back to training and that’s what everyone is thinking about.
“We’re hungry to hear that song once again. It’s time.
“We have the quality to do it, so we have to make sure we will do it.”