He ticked off a penalty against Tigers enforcer Stefano Utoikamanu for a high fend and backed the bunker's decision not to overturn a South Sydney try against where two players appeared to be offside.
Rabbitohs five-eighth Cody Walker and fullback Latrell Mitchell combined for that try, but Annesley didn't find any conclusive evidence the bunker could have used to reverse the decision given a touch judge in line with the kick ruled them both onside.
The call came with the Dragons looking to get back into the contest trailing just 14-10 in their 24-14 loss.
It prompted some Dragons fans to declare that officiating had cost their side the match while Tigers playmaker Adam Doueihi took to Twitter to label the refereeing performance in his side's game a "joke".
"This game has this unique history and habit of zoning in on one decision by an official and that's why we lost the game, and frankly, it's rubbish," Annesley said.
"Referees are using their judgment to call players onside or offside ... they're really tight decisions, they will divide opinion.
"But to come out publicly and say 'that was wrong' and 'that single decision cost us a game', I just think it's way over the top.
"(There are) a very small number of games where ... incorrect actions of the officials influenced the outcome. It does happen, but very rarely."
Utoikamanu was reported for his high fend but not cited by the match review committee, however Annesley said he had "no problem" with the referee's decision given he saw illegal contact to the head and neck.
He was similarly strong defending the bunker's decision to award Walker's try.
"For the bunker to overturn this decision of try, remembering they've got a touchline official right in line with it saying Latrell's onside ... they just can't do it, it's not possible," Annesley said.
"So to say this is an incorrect decision and to roundly criticise the officials for this, particularly the bunker for this decision, is just completely unfair.
"What we've seen over the course of the weekend is a degree of criticism levelled at match officials which is unwarranted.
"As I've said many times, controversial decisions do not necessarily mean wrong decisions, it just means that they're tight."
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