Coach Clayton McMillan said they were likely to be without him for at least two weeks, but they also lost lock Jimmy Tupou, who appeared to have a fractured eye socket.
McMillan said the Waratahs' start challenged the Chiefs but was proud of how his side fought back.
"It challenged our guys around being physical, especially early. Both teams came with that mindset, and we're winning that battle. But we were a little inaccurate and paid the price early.
"We stayed composed and got a couple of opportunities late in the first half that got us back into an even ballgame and we were happy with that."
The Chiefs respected the Waratahs and believed they were a better side than their results have shown.
The game was also a defensive challenge for the Chiefs, who had their game undone by the Hurricanes, and they spent time during their bye week addressing issues that were exposed.
"It was good to see a response today."
The tackling of flanker Samipeni Finau came under scrutiny again when he clattered Waratahs first five-eighths Tane Edmed just after he had got a pass away. The tackle was deemed safe by match officials but has been the subject of attention by Australian fans.
McMillan said the tackle was clean. It wasn't a deliberate strategy for Finau to target five-eighths. He was more concerned about the consequences if Finau erred in getting his tackle area too high.
"We're talking about a difference of about that much [10cm]. He has an acute awareness of the small margins and could be off the field. He's an important player for us, so he needs to get it right.
"We don't want to stop any of our guys from getting off the line and getting a good shot on if they can within the laws of the game. And you see multiple collisions in the game that border on being on the wrong side of the law.
"It's a fine line. It's a brutal sport at times. You don't want to suppress your players from trying to dominate those collisions physically, but there is a responsibility on them all to make sure that they're accurate, and sometimes they get it wrong, and they pay a heavy price, individually and collectively.
"We don't want that to happen. Safety is always paramount, but we don't want to suppress them from going out there and being physical."
McMillan said the Chiefs' five-eighths, Damian McKenzie, copped the same attention every second week. And while the attention, in this instance, was on a tackle, there were also the breakdowns, which were dynamic and put people in vulnerable positions where massive collisions occurred.