The stand-off between the Belgium global and Everton intensified when he publicly questioned the club's level of ambition following his contract rejection.
Lukaku, whose current deal runs to 2019, knocked back Everton's £130,000-a-week offer.
Though they did not go down, Stalybridge were facing relegation from the Conference North into the seventh tier of English football, so the prospect of becoming a Premier League footballer must have seemed very far away at the time.
Everton now sit seventh in the Premier League table, two points behind Manchester United though the Old Trafford club have two games in hand.
"It is hard to always keep that momentum at home but we'd like to do it".
"To do that, you need the platform to show yourself", he said when asked about his desire to be ranked along with the world's best forward.
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Dominic Calvert-Lewin finished off a fine Everton move after eight minutes to slot home his first top-flight goal.
However, a harsh decision by referee Paul Tierney to dismiss Tom Huddlestone for a lunge on Idrissa Gueye enabled Everton to wrap-up the points in style late on, although Koeman acknowledged that Hull presented a tough challenge.
"We would like to continue the momentum. But the final result didn't reflect what happened on the pitch", Koeman added.
At home the Dutchman's more pragmatic, direct approach has already garnered 31 points from a possible 42 and they have lost just once there in the league in the last 12 months - against Liverpool in December.
The three previous players to do so are Robbie Fowler, Michael Owen and Wayne Rooney - so he is the first foreigner to rack up so many Premier League goals at such a young age.
Hull boss Marco Silva, meanwhile, agreed with his counterpart's assessment of the red card incident, insisting that his side did not deserve to lose by such a margin. "It decided the game".
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