Koeman believes the striker spurned chances in the club's 2-1 league win at West Bromwich Albion on Saturday. Lukaku also couldn't find the back of the net in Tuesday's 4-0 rout of lower division side Yeovil Town.
"It's always part of the job if strikers are not scoring, then the manager gets questions about the striker. I don't look backwards about Lukaku and what he did last season because that's not my problem," Koeman told British media.
"My problem is now and he didn't score against West Brom. He had one big chance. He had some good chances last Tuesday, but I'm not worried about that. Maybe if he doesn't score in the next then ask me that question then."
The 53-year-old Dutchman added that Lukaku, who withdrew his request for a transfer last week and committed his future to Everton, will need better service to make an impact.
News that makes sense
Your trusted source for staying up-to-date with the world around you. Get free daily news updates and analysis, straight to your inbox.
"Strikers need always support to get crosses, to get passes and that's all about the rest of the team. Sometimes they can create a big chance for themselves," Koeman added.
"He's that player that needs support but also he can score by himself because he has that quality."
Everton, who have four points from their opening two league games this season, host Stoke City on Saturday.
(Reporting by Ian Rodricks in Bengaluru; editing by amlan Chakraborty)
