The 27-year-old later played the full 90 minutes on Tuesday night in West Ham's 1-0 victory over Watford, where he was booed by sections of the crowd.
On Wednesday, the club confirmed that Zouma will be fined two weeks' wages amounting to £250,000 for the incident and the money will be donated to animal charities.
When asked about the situation by Sky Sports, Antonio replied: "I've got a question for you: Do you think what he's done is worse than racism?"
"I'm not condoning a thing that he's done. I don't agree with what he has done at all. But there's people that have been convicted and been caught for racism and have played football afterwards.
"They got an eight-game punishment or something like that, but people are now calling for people to be sacked and to lose their livelihood.
"I've just got to ask this question to everyone out there: Is what he's [Zouma has] done worse than what the people convicted of racism done?"
A spokesperson for the Royal Society for the Prevention of Cruelty to Animals (RSPCA) also announced on Wednesday that Zouma's pet cats have been taken into care.
English fifth-tier club Dagenham & Redbridge confirmed on Thursday that Zouma's brother Yoan, who filmed the video, has been dropped.
A statement read: "Yoan was this week contacted by the RSPCA to assist in their investigation and is fully cooperating with them.
"However, Dagenham & Redbridge FC would again like to reiterate that it condemns any form of cruelty towards animals and fully understands the reaction of many of its supporters.
"The club has therefore decided that until the RSPCA has completed its investigations, Yoan will not play for Dagenham & Redbridge in any competitive match.Any further action deemed necessary to be taken will be made at the conclusion of the RSPCA investigation."
Meanwhile, Vitality, West Ham's official wellness partner, has suspended its contract with the club as a result of the video, and Adidas also confirmed that "Zouma is no longer an Adidas contracted athlete."
Another club sponsor, Experience Kissimmee, also said it has ended its sponsorship after learning that the player had started the game.
Information from Reuters was included in this report.