Lukaku scored 87 times in 166 appearances for Everton between 2013 and 2017, before Manchester United paid £75m to sign the Belgian international ahead of the new campaign.
The 24-year-old has six goals in six appearances for the Red Devils this term, and Koeman has conceded that his club have been unable to replace the forward's goals amid their early-season troubles.
"I don't say impossible but that was close to impossible to get someone in who will score that amount of goals that Romelu scored for Everton," Koeman told reporters.
"With Romelu we had enough fights about how he needs to press, how he needs to run, how he needs to move but in the box, with opportunities to score, he is one of the best.
"It is always difficult to replace players like him because of the person he was, the physical boy that he is, the number of goals that he scored. It is difficult."
Everton will travel to United in the Premier League on Sunday afternoon off the back of a five-game winless run in all competitions.