The midfielder, who recently resigned with PSV, has revealed his disappointment after the 28-year-old was booed during Tuesday's friendly at the Allianz Arena
The Dutch national side faced the German giants at the Allianz Arena on Tuesday to serve as closure to the dispute between the two parties over an injury sustained by the attacker during the 2010 World Cup.
Robben, who appeared as a substitute versus his parent club, has come under criticism from FCB supporters following his injury-time penalty miss in Bayern's Champions League final defeat to Chelsea last Saturday.
However, the 28-year-old has been defended by Van Bommel who is adamant his compatriot should consider his future at the club over the incident.
"It's a disgrace. When you look at what Robben has achieved in his career. He led Bayern to the final at Madrid and is so important to the club. Bayern should be really happy to have a player like him," the veteran told SBS6 after the match.
"Arjen has signed a new three-year contract but if I was him I would think twice about my future. I don't know what Arjen will do, but I would think about leaving the club if I was him.
"Nobody from the club supports him, I'm the only one that supports him in the press. Mentally he is very strong. Everytime something bad happens to him, he comes back stronger."
Netherlands coach Bert van Marwijk also weighed in with his thoughts on the situation, stating: "The reaction of the fans annoyed me. I'm very disappointed, treating your own player like that. It's a disgrace."
Goals from Klaas-Jan Huntelaar and Luciano Narsingh were not enough for Netherlands as Toni Kroos, Nils Petersen and Mario Gomez all struck for Bayern.
The Oranje will continue their preparation for Euro 2012 when they face Bulgaria in a friendly on May 26.