He acknowledged that the council's investment in the museum was cut significantly about 14 years ago.
"I understand it was a high percentage of the museum's operating fund received previously," he said.
"The museum has been catching up ever since - it's always a bit behind the eight-ball."
In recent times the council had not reduced the operating fund and five or six years ago there had been funding for a natural history curator, McDouall said.
However, while the museum was closed for earthquake strengthening there would have been no point engaging a new person for the role, he said.
"It only reopened in March 2019 and since then I think we've been pretty responsive to the museum's asks. But we've put the acid somewhat back on them, saying why are we the only funder? There are numerous pots of funding that could be sourced."
The museum receives some funding through Ministry of Education contracts.
Before Labrum's appointment, the museum's acting director had told the council capacity issues were a hurdle to making funding applications, McDouall said.
"I'm really very supportive of the museum - it's a wonderful taonga for the community.
"I'm very supportive of getting an iwi/Māori collections curator. I think that's the right decision. They are taking more and more of these incredible taonga and looking after them so it's a pretty extraordinary collection of artefacts."
McDouall said the museum governance board and council, as funder, were totally separate and he had confidence in the museum's governance.