The win was not without controversy when the TMO denied Anscombe his fourth try for the night and awarded the Rebels two tries from what appeared to be forward passes.
Despite that, the Chiefs came away with the maximum five points.
When questioned about the TMO's performance, Rennie said: "I struggle to see fault with Gareth's last try, and [there were] a couple of dodgy decisions.
"Our issues are ours and we have a couple of things to sort out, but I thought it was pretty poor."
He intended to follow up the TMO performance with Sanzar referees' boss Lyndon Bray.
The Chiefs had 10 players out injured on Friday night and Rennie felt he could tidy his team up with selection pressure, once more players were fit.
"If you don't have many injuries you can field a similar team each week," said Rennie.
That is not a luxury that extends to the Chiefs at the moment. From the large injury list, Tawera Kerr Barlow is expected to return this weekend and prop Ben Afeaki is a possibility.
The Chiefs will head to Pukekohe to take on the Western Force on Friday and dynamic midfielder Tim Nanai-Williams called for a big crowd from his local supporters on the night.
"I know that the boys are excited, as I am, about bringing Super Rugby to the northern part of our franchise," he said. "It will be a real privilege to play for the Chiefs on my home ground.
"We got such great support from the public when we played at Pukekohe last year ... So I'm really hoping the locals will rally behind us again and come out to see the boys in action."