Defender Aogo, a former Germany international, flew to the Spanish island to meet his agent while Venezuelan midfielder Rincon went there for family reasons after coach Thorsten Fink gave his team two days off following their heavy loss.
"We do not give two days off so that people fly to Mallorca but so that they can think about how they can become better," Fink told reporters on Wednesday after announcing their exclusion.
Hamburg have made a rocky start to the Bundesliga season with just one point from their first two games and have already conceded eight goals.
"In principle the players can do what they want on their off days but to go to a party island after such a bad performance is a bad sign," said Hamburg sports director Oliver Kreuzer. "This is something we cannot tolerate."