According to German newspaper Bild, Djourou and Behrami came to blows in Hamburg's dressing room on Saturday, with Peter Knabel's men trailing 1-0 and on their way to a fourth straight defeat.
Hamburg went on to lose 2-0 - with Djourou sent off in the 88th minute - and they finished the weekend in last position in the Bundesliga standings, one point adrift of 17th-placed Stuttgart, who defeated Werder Bremen 3-2 on Sunday to rise off the bottom.
"There was an emotional dispute. It was discussed. It is regulated. Whoever breaks discipline must be punished," Beiersdorfer told Bild.
After Saturday's loss, Hamburg captain Heiko Westermann conceded his team's second-half display was "not Bundesliga worthy", while midfielder Lewis Holtby was filmed angrily confronting the club's fans, seemingly frustrated at allegations he was not trying.
"I spoke to our fans after the final whistle, it was very emotional," he told Hamburg's website.
"I can understand that they are gutted but we have to stick together and not go our separate ways.
"I am the last person here who wants to be relegated with such a tradition-steeped club. The whole team doesn't want to."
Those matches will be followed by three consecutive fixtures against fellow bottom-six clubs - Mainz, Freiburg and Stuttgart - before a clash with Schalke on the final day of the season.
"There are still a lot of points left to fight for, and we will be playing teams close to us in the table again, all of this gives me reason to hope," Holtby said.
