Barca sit ninth in La Liga having lost four of their first 10 league games and Tuesday's 3-0 defeat to Juve cost them top spot in their Champions League group.
Following the loss to the Italian champions, a report in the Catalan press claimed the players are uncomfortable with Koeman's 4-2-3-1 system and have asked him to consider reverting to 4-3-3.
"That is not true, it's a lie," Koeman said in a news conference ahead of Sunday's game against Levante at Camp Nou. "The players would have said. We speak."
"I feel supported by the players. If I didn't have their confidence, I wouldn't be able to do my job.
"So I feel comfortable, although worried about the situation in the league, as any coach would be. We must improve things.
"Results aren't at the level expected. We're lacking concentration at set plays and throw-ins. We must be more aggressive in certain moments. We're the team that creates the most chances, but we don't take enough. Add all that together and it explains the losses we've had."
Barca's return of just four wins and two draws through their first 10 league games is the club's worst start to a domestic campaign since 1987.
But Koeman dismissed the suggestion his side's failings on the pitch could be psychological and called on the older heads in the squad to stand up ahead of three home games in the space of a week -- Real Sociedad and Valencia follow Levante.
"This team has enough personality and experience," Koeman added. "It's a moment for the experienced players who've been here for so many years to step up. The good players always stand up.
"I don't believe in psychologists and mental [issues]. If you play for Barca, pressure exists, you know that, and you have to overcome it."
Koeman did show some sympathy for Barca's supporters, though, acknowledging that it's a hard time for the club on and off the pitch, with poor results coming amid financial problems and the uncertainty of not knowing who the next president will be until the election on Jan. 24.
"It's difficult for [the fans] because if most of the time [you are] on top, winning titles, then it's difficult to understand why we lose against Cadiz or Getafe," he said.
"Sometimes it's difficult to explain. The whole situation of the club is a difficult one: not sure about Covid, about the financial situation, there's a new president coming in next month. A lot of things are not sure at this club and it's always difficult to have the trust and to have the rest to be a winning team."