L'OM have slipped to sixth in the Ligue 1 table following back-to-back defeats to Paris Saint-Germain and Nice and face a crucial game on Friday night away to Reims, who are just one place and one point below them.
Asked whether he feared his players were coasting to the end of the season - which is swiftly followed by the World Cup in Brazil - Anigo told reporters in France: "I would like to say no.
"I cannot guarantee anything in that regard, much as I would like to tell you otherwise.
"Some have individual objectives, others are playing for the club to finish as high as possible. We have to hang on until the end."
Players including Andre-Pierre Gignac and Andre Ayew disregarded an instruction from Passi to stay behind for extra work following the conclusion of Wednesday's training session.
But Anigo dismissed concerns over the incident, insisting the players had completed their scheduled recovery work.
"They had effectively completed the work set for the session," he told L'Equipe.
"It was a day of recuperation and fitness work. Franck wanted them to do more but it was not scheduled in the training programme."
Speculation still surrounds the identity of Marseille's coach for next season, with Italian Luciano Spalletti recently linked with the role after leaving Russian club Zenit St Petersburg.
Sporting director Anigo succeeded Elie Baup in December in an arrangement lasting until the end of this season and is not worried by speculation over the team's future direction.
He said: "Everyone speculates. It was clearly announced when I took the role that there will be another coach at the end of this period.
"The club will confirm the arrival of the new coach at the end of the season. That's normal. What is certain is that I will finish the season."