Marschall lodged a complaint with the match officials after the incident in the 65th minute of the Championship clash.
With West Ham trailing 2-0, Argentinian Castellanos came to close down Marschall as he held on to the ball.
The players clashed and Marschall, on his Championship debut, then appeared to point at his shirt, gesturing he had been spat at.
"I haven't asked him about it, but it's like anything else, I'm sure there'll be footage of it, or not of it if it didn't happen," said Millwall manager Alex Neil.
He added: "I didn't know what had happened, I'd just seen Filip walking out with the ball and thinking, 'Where's he going?'
"And then the fourth official basically said that there was an accusation of spitting. So, yeah, I don't know."
Castellanos could face a six-match ban if he is found to have spat at Marschall, which would be a huge blow to West Ham's promotion bid.
Hammers boss Nuno Espirito Santo said: "I'm aware of the allegation, I didn't see the images, I didn't speak with Taty.
"I cannot go much further on that, I'm sorry. For me to answer that, I have to see it. I'm going to look at the images. I cannot answer."
The allegation was a sour twist to a first meeting between the fierce London rivals in nearly 15 years.
Millwall led at half-time through goals from Caleb Taylor and Camiel Neghli.
But in a vastly improved second-half display the visitors hit back through Mohamadou Kante and Konstantinos Mavropanos.
West Ham looked likeliest to find a winner until last man Kante was sent off for pulling back fellow substitute Kyrell Lisbie as he raced through on goal.
"Clearly the first half we didn't do well in the game, we didn't start well, we were not precise and lost balls," said Nuno.
"We didn't deal with the physicality of Millwall, they are so good and so strong."
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