"If you look to the team this Saturday and the bench you cannot compare it to the big six".
Everton welcome Stoke City to Goodison Park in the Premier League on Saturday afternoon, and are favourites to come out on top with the Blues so strong on home soil compared to the poor form of Stoke on the road.
The enthusiasm of early summer has given way to anxiety at Everton.
"Okay, I believe if we get the picture of the last season we are stronger but being stronger than last season does not mean you will win against the big six because they also will be more strong than last season".
Koeman has experimented with two different formations in pre-season, and it may take some time for a decision to be made which best suits the players at his disposal.
Everton also signed Sandro Ramirez from Malaga, who scored an impressive 14 goals in 30 appearances last season. They are tasked with the giant responsibility of replacing Romelu Lukaku.
"If there is a club thinking we can wait until the last day and we put some money on the table and we get Ross Barkley, sorry, you do not get Ross Barkley".More news: Trump Increases Rhetoric on North Korea, As His Aides Fight It Out
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"I don't say impossible, but 25 goals is a lot and we have to find other ways and productivity from other players and we like to bring in other players in".
Everton's last four Premier League campaigns have all started with a draw, with three of those ending 2-2.
Lawrenson added that he is looking to see a better start to the season for Stoke having struggled early on last season, but he isn't seriously anxious about their fortunes this season.
"But still now we really have one striker, in my opinion".
Wayne Rooney returning to Everton is massive news for the club and the reception he'll receive should have Goodison shaking.
Having said that I'm backing them to kick the season off with a win against a Stoke side I fear will struggle having lost Marko Arnautovic to West Ham.
"They've got a good side and they've spent money from letting good players go, perhaps similar to Southampton a couple of years ago. We are looking forward to getting started".