The Dutchman's Saints have spent almost the whole season in the Premier League top four but four consecutive league defeats and another in the League Cup have been a harsh reality check.
With a frantic fixture list and a squad beginning to creak under the strain, pessimists could argue that Southampton's almost inevitable descent down the table has begun.
Koeman, however, remains upbeat, even if he will be without the likes of suspended Morgan Schneiderlin and Victor Wanyama and injured Dusan Tadic for Saturday's home clash with Everton.
"If somebody told me in pre-season that in the middle of December we'd be fifth, I'd say give me the paper and I'll sign it now," Koeman told reporters on Thursday.
"I know my players and I know how they can play football. Maybe it's about freshness and changes in the team."
The first three of Southampton's defeats were against Manchester City, Arsenal and Manchester United, but they then lost to struggling Burnley before bowing out of the League Cup quarter-finals this week to third tier Sheffield United.
"I'm very disappointed about how we lost against Sheffield United," Koeman said. "That's the first time I'm disappointed in the team's spirit.
"But the nicest part of football is that there's always the next game."
With the January transfer window about to open, Southampton have been linked with several high-profile players including Galatasaray playmaker Wesley Sneijder, but Koeman knocked back suggestions his fellow Dutchman could become a Saint.
"I'm interested, but I know we can't pay him," he said. "There's nothing in it."
(Reporting by Martyn Herman; Editing by Ken Ferris)
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