The striker, on loan from Chelsea, scored the winning goal in the 3-2 victory over West Ham on Saturday but clashed heads with Joey O'Brien in the process.
He required lengthy treatment and confessed afterwards that he had no recollection of his debut strike.
"I remember nothing about it," the Belgian said.
"I was out of it and the first thing I asked the doctor was, 'who scored?', and he said, 'you did'."
The visitors twice had to come from behind at Upton Park to preserve their unbeaten start to the season, with Leighton Baines scoring two stunning free-kicks before Lukaku, on as a half-time substitute, netted the decisive goal with five minutes to play.
And manager Roberto Martinez, who saw his side finish the match playing against 10 men following Mark Noble's dismissal, was full of praise for his match-winner.
"I think Romelu's the type of striker that influences everyone around him," he said.
"I thought Kevin Mirallas became a threat all of a sudden with his pace behind Romelu but I thought the goal was everything that typifies Romelu Lukaku; that desire and that character to want to be successful and that's why he's going to be such a big asset for us.
"He's a very, very intelligent footballer and all I want is for him to carry on enjoying his football but also go from strength to strength because his potential is incredible.”
The result means that Everton are now the only team in the Premier League yet to suffer a defeat, but Martinez insisted that he and his charges are taking nothing for granted.
"The dressing room that we have is a very special dressing room and that's a great label to have (being unbeaten) but it's something that we'll have to work really hard to extend it," he added. "You don't win anything in September, unfortunately."
