Koeman is under pressure with his side 14th in the Premier League and struggling in Europe.
Everton were booed off after being held to a 2-2 draw at home by Cypriot minnows Apollon Limassol in the Europa League on Thursday.
They did gain a lift – and climb out of the bottom three – by beating Bournemouth 2-1 last Saturday, but the manager has admitted his team are short on confidence.
Koeman’s side need a home win over Burnley in the Premier League on Sunday to ease the growing sense of crisis at Goodison Park going into the international break.
And the boss is adamant that he still has full belief in himself to turn their season around.
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He said: “I am too long in this job to lose my confidence. Yes, I am worried about how we turn this situation round but I have enough confidence to be the same manager I was for the last six or seven years, and I was successful.”
Koeman said he had no argument with the fans booing after Hector Yuste’s late equaliser on Thursday gave Apollon Limassol a point and left Everton bottom of Europa League Group E after two games.
“I respect every opinion of Everton fans,” he said. “It’s easy to support a team when they are winning. It’s more difficult when they are not.
“But that’s in every place, in every club. The fans are allowed to react and be frustrated. I was frustrated yesterday. That is normal.”
Koeman is likely to be without defenders Phil Jagielka and Michael Keane once again for the visit of Burnley.
Keane has missed the last two matches with a foot injury, while club captain Jagielka has a hamstring problem.
But Wayne Rooney is available to play despite needing painkillers to get through Thursday’s match after damaging his wrist during a first-half fall – as scans have shown no fracture.