Rochdale prevailed by a 1-0 scoreline and at the full-time whistle, some fans ran onto the pitch and goaded the travelling Millwall support, who remained in the stands.
Harris has also claimed that he, his staff and players were abused, and the events are likely to lead to the Football Association launching an investigation.
The 40-year-old is quoted by the Daily Mail as saying: "I thought the Rochdale fans were a disgrace at the end.
"Our fans were goaded, it wasn't quite right. My players were treated very badly, and me and the staff were abused. As a football club, we have the stick pointed at us fairly often."
Rochdale will now face the winners of the tie between Newport County and Tottenham Hotspur.