We know the Blues have designs on a top four spot - something which can not be scoffed at, especially after Leicester City showed anything is possible by winning the 2015/16 league title.
"I know the expectations are higher than last season, but I always look to be realistic", said Koeman.
"To replace Lukaku is really hard", said manager Koeman.
Stoke City, on the other hand, has not had a massive transfer window.
Despite a significant outlay, manager Ronald Koeman says his squad is not yet comparable to the top six.
Everton will hope to get off to a good start at home as they seek to finally qualify for the Champions League.
Everton have yet to receive any bids for their homegrown midfielder, despite his entering the final year of his contract and refusing to sign a new deal. They have had a busy summer, signing seven players.
Xherdan Shaqiri's Stoke have not recorded back-to-back away league victories since October
Everton improved after the break but issues with fluidity and cohesion remained for Koeman's new-look side, with Jordan Pickford forced into an outstanding save to deny Xherdan Shaqiri a last-gasp Stoke equaliser.
Before all that though, the Toffees at least get to start the league season at Goodison Park, versus Stoke City. We must all concentrate on getting a good league run going and achieving some consistency in the Premier League.
Yannick Bolasie and Ramiro Funes Mori continue to recover from long term injuries while Aaron Lennon is still doubtful after being held out of the Europa League qualifier last week.
After 13 record-breaking years at Manchester United, the 31-year-old made the ideal mark on his Premier League homecoming.
The Toffees have scored 30 Premier League goals at home in 2017, more than any other side - and five more than they managed in the whole of 2016.More news: What Does the US Military Do on the Island of Guam?