Investigations are under way by both Health New Zealand and police after the incident in Hamilton earlier this month.
The girl, who is reportedly autistic and non-verbal, was mistaken for a 20-year-old mental health patient by police after she was seen climbing a bridge.
Doocey told Morning Report the situation was hugely distressing.
"The 11-year-old was taken into Waikato Hospital and administered antipsychotic drugs twice throughout the day," Doocey said.
Asked how this could happen, the minister says the issue sits with the misidentification of this child.
The 20-year-old she was mistaken for was under compulsory care in the community, which is why the antipsychotic drugs were able to be administered, Doocey said.
How the misidentification process failed was needing to be investigated, he said.
"I still don't understand how an 11-year-old can be confused for a lady in her 20s."
Both Health New Zealand and Waikato police have launched internal reviews.
Doocey first became aware of the incident on Friday, he said from the information he received the incident had gone to a review committee but "it doesn't look like that review had started".
"It looks like the incident review wasn't done almost two weeks after the event."
Doocey said not only would people need to be held accountable but the system needed to be.
Asked on Tuesday whether heads should roll, Prime Minister Christopher Luxon said: "By all means, there should be accountability in the system."
Police Minister Mark Mitchell has said officers were "doing the best that they could".
"The police, unfortunately, throughout the process, have misidentified her, but make no mistake, they were doing the best that they could to look after her and to support her."
The Health and Disability Commissioner and the Independent Police Conduct Authority have both received complaints about the incident.
