"Not for me," he said. "I think the pressure is always there in football, because you like to win and you put yourself under pressure to win the game.
"Everything which is mentioned from outside is out of hands; I can't stop it and I can't do anything about that.
"Every Premier League game is a tough one regardless of the name of the opponent."
Everton have leaked 12 goals in their seven games to date but Koeman feels that statistic gives a false impression of his team's defensive capabilities.
"I think it's more a question to be answered halfway through the season because we've played four title contenders," he said.
"It's difficult because everyone expected difficult results but I did not see my players between after the game against Burnley and either yesterday or today (Friday).
"You need a little bit of luck; you need to score the first goal in a game and we need to change that.
"The fastest way to change that is by being a professional and working hard."