The Toffees are looking to return to winning ways against Bournemouth after their midweek defeat to Norwich City in the EFL Cup.
But Koeman is happy with the start his players have made under his tutelage.
“It's a good start to the season, maybe better than everyone expected," he said. “We have a strong team and we will keep working hard every day to improve. The quality players can make the difference. We did not have that productivity on Tuesday but before that, we had.
“I was not happy about the result. I was comfortable with that they showed but, of course, it was not good enough because we did not score a goal. We need to accept it because we have had a good start to the season."