Jeff Hendrick's first-half striker means that the Toffees have won just once since the opening day of the season, with four losses in five Premier League games leaving Koeman's side just two points above the relegation zone.
However, following the defeat, the Dutchman told 'Sky Sports': "I'm not unhappy what I saw from the team, they showed today how we have to play.
"If you play against a team who are defending so strong you need to be at your best. We didn't have that creativity.
"We don't have that type of player at the moment. Maybe Gylfi Sigurdsson or [Wayne] Rooney. Sigurdsson had that big shot at the beginning but we don't really have that creativity to bring them down in such a defensive shape."
When asked if his players lacked confidence after going behind, Koeman added: "You always get a reaction, that's normal in this situation.
"It impacts the team, the fans, but I can't complain about the attitude or commitment of my players today. That was perfect. Of course we can play better on the ball.
"In this situation it is really disappointing but it's a different defeat than previous."
Everton had a penalty shout in the final stages when Rooney flicked the ball on to Matthew Lowton's arm, and the Everton boss said: "You know, sometimes you get the help of a referee.
"I don't say it was a penalty because it wasn't his intention to touch the ball - but on other occasions I've seen a penalty given.
"This situation is really disappointing. But we'll continue because what I saw today is how to come out of this difficult situation.
"I understand the whistles at half-time and I understand everybody is really disappointed by the final result."