Lukaku, 24, joined Manchester United in July for a reported £75 million, ending a four-season stay at Goodison Park.
Man Utd and Everton to draw at 4/1
The Belgium international scored 25 league goals last season, and he has netted six in six in all competitions for United.
Koeman, whose team have made a slow start to the campaign and visit Old Trafford on Sunday, said replacing Lukaku was always going to be a huge ask.
“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,” the Dutchman said, via the Liverpool Echo .
“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 made numerous signings, adding the likes of Wayne Rooney, Gylfi Sigurdsson, Davy Klaassen and Sandro Ramirez.
However, they have scored just two goals in their first four league games, and were humbled 3-0 by Atalanta in the Europa League on Thursday.
