The Ingolstadt defender reported the incident to referee Florian Meyer during his sides 1-0 defeat to their Bavarian rivals on Saturday.
It led to the game being temporarily halted while an announcement was made warning the abuse to stop.
But Da Costa believes it was an isolated issue, and not part of a wider issue in Germany.
"Several people felt the need during the throw-ins or any contact with the ball to shout stuff like 'n*****' or 'Black Pig' in my direction," he told SID.
"Every time the ball came near me, there were monkey chants.
"I told Mr Meyer that I was being viciously insulted, that this was no longer acceptable for me.
"I think it was an isolated incident, that it never happened before. It is not a specific problem of 1860 fans.
"I think actually in Germany these things are quite well under control, but if some idiots get out of line, there's nothing you can do. If you drag the normal fans into this, it wouldn't be fair."
The Munich outfit released a statement condemning the abuse, and warned their fans such incidents would not be tolerated.
"Any abuse of this kind has no place in our games," 1860 chief executive Robert Schafer told the the club's official website.
"We are very grateful to our stewards who responded immediately and professionally.
"We were able to identify the person and have (reported) his behaviour to the police.
"Moreover, we will promptly issue a stadium ban. Each case of this type is one case too many.
"People with such ideas are no lions fans. We have zero tolerance on this topic and condemn (the actions) in the strongest terms."
