Barca, runners-up in last season’s La Liga title race, were beaten 1-0 at Getafe on Saturday, two weeks after the Blaugrana drew 1-1 at home against Sevilla before the international break.
Barca’s form sees them sitting ninth in the Spanish top flight with seven points, though they have two games in hand over league leaders Real Sociedad, who have 11 points.
And Koeman, appointed this summer, has admitted that his captain and talisman has not been at his best in recent weeks.
“Maybe, at the moment, Messi’s performances could be better,” said the Dutchman – a former Barca player himself.
“But he is happy, he is working hard and he wants to be the captain.
“I don’t have a single complaint. He has also had some bad luck; he hit the post [against Getafe] and on another day that goes in.
“I don’t have any doubts about his performances and we’re going to see him [at his best] in the upcoming games, I’m sure.”
Messi’s contract at the Nou Camp expires next summer, though he tried to force an exit in August – only to back down due to his desire to avoid taking his club to court.
Fellow forward Luis Suarez did leave, however, joining La Liga rivals Atletico Madrid last month after being deemed surplus to requirements by Koeman.
Messi publicly criticised the handling of Suarez’s departure, with the Argentina captain’s relationship with Koeman seeming frosty in its infancy.
Barca next take on Ferencvaros in their Champions League group-stage opener on Tuesday evening.
That game is followed by El Clasico at home to rivals and La Liga champions Real Madrid in the Spanish top flight on Saturday.