Bale was substituted during the 1-0 defeat by Barcelona on Saturday at the Santiago Bernabeu and suffered whistles and jeers from his own supporters.
Real, who lost 3-0 to Barcelona on Wednesday to suffer Copa del Rey elimination, are third in La Liga, 12 points behind their arch-rivals who lead the standings.
"This generation of Real fans will be talking about Gareth's goals for years to come. Frankly they should be ashamed of themselves,” Bale’s agent Jonathan Barnett told Sky Sports News.
"Gareth deserves the greatest of respect. The way the Real fans have treated Gareth is nothing short of a disgrace.
"In the six years he has been in Spain, he has won everything. He's one of the best players in the world. Those fans should be kissing his feet."
Bale, 29, has won the Champions League four times with Real Madrid after joining for a club record 100 million euros (86 million pounds) fee in 2013.
He has failed to win over supporters despite scoring crucial goals for the club and has been criticised in the media for failing to learn Spanish and integrate with his team mates.
(Reporting by Rik Sharma, editing by Ed Osmond)
