"He said 'watch him', in other words 'keep an eye on him' but that is not good enough.
"That is saying 'I have identified that there is an issue there so keep an eye on him'. Well, keep an eye on him is not the right answer."
"It is a very serious error in that we hold clubs accountable for dealing with suspected head injuries and we hold them accountable to a very high degree. We know from the audio that they (the referees) identified this, they just didn't take the right action at the right time."
Annesley also confirmed that the bunker officials had incorrectly denied Warriors wing Ken Maumalo a try.
The bunker should have relied on the first camera angle which confirmed the try was scored by a diving Maumalo, who scored two others in the Warriors' victory.
And a stripping penalty against Adam Blair had also been incorrect, as it was a loose carry by Mason Lino.
There were two errors against the Wests Tigers in their loss against the Roosters, involving a charge down and a foot in touch before a try.
Annesley said: "I need to get comfort from the people I have to hold responsible for the performances of match officials," he said.
"The one thing we can't stop is mistakes but some of mistakes over the last couple of weeks simply aren't good enough and they are mistakes that shouldn't have been made so we need to try to find out why and what they are doing to hopefully ensure it doesn't happen again leading into the finals.
"That is what coaches do week in and week out, they don't accept errors from their players and they work on strategies and ways to try to make sure those mistakes aren't repeated."
But he praised the bunker officials for spotting Cronulla's Kyle Flanagan kneeing Bronco Matt Lodge in the head. Flanagan escaped a suspension with an early plea,