Everton has spent a lot of money in the transfer window and they will look to so well this season as a result of it.
A superb save from Pickford, denying Xherdan Shaqiri in the closing moments, ensured Rooney wasn't denied his winning return.
"They are notoriously slow starters though, and I don't see that changing".
Everton beat Stoke City narrowly to break a four-game streak of opening day draws.
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McCarthy, who has been linked with a move away from Everton, sat out the final pre-season friendly against Sevilla on Sunday with Koeman insisting the former Wigan player wasn't fit.
Everton are unbeaten in three games against Stoke (W2, D1), having lost the previous three. Substitutes from either side opened up the game in the last quarter, and once again Everton had chances on quick counter attacks but failed to take advantage of the additional space. Their only defeats came against Liverpool and Chelsea.
A revitalised Wayne Rooney is relishing a new lease of life at Goodison Park after scoring the victor in Everton's 1-0 victory over Stoke City in their opening Premier League game of the season.
The glow from Rooney's 199th Premier League goal was nearly erased when Fletcher went close to equalising after half-time with a stinging strike.
The Premier League match between Everton and Stoke will be broadcast live on CNBC.
"If you look to the team this Saturday and the bench you cannot compare it to the big six". He last scored in West Brom's 3-2 home victory over Crystal Palace in February 2016.