His side beat Stoke at Goodison Park this afternoon 1-0, but Koeman says the side need to improve on their ability to kill off games and not feel nervous at the end of the game defending a 1-0 lead.
“Overall I think the three points are deserved,” said the boss.
“More ball possession, more shots on target, while Stoke had zero.
“At the end at 1-0 it’s always difficult because we had to defend all the time, but we had opportunities to kill the game in the second half but we didn’t.
“That’s always difficult but I think the workrate, the belief and the spirit of the players was fantastic.
“I can understand why maybe Mark Hughes will be angry.
“If every referee gives a penalty for this kind of situation then you can accept it, but one referee yes and another no, and that sometimes makes it very difficult to understand.
“It’s always difficult to come to a new club, you need to change a little bit. Maybe the players need to change in the way we like to work, but they’re doing the best and doing everything to improve.
“It’s not the end, it’s a good start to the season but we need to improve more in several aspects; how we press, h0w we kill the game and how we improve in the box.”
When asked about transfer business, Koeman said he was hopeful that he would bring more new players into Everton, adding, “If we don’t sign anybody before Wednesday then I’ll be disappointed.”