"We've just got to deal with decisions that are made on the field," he said.
"That's what we talked about as a group and we knew going into this game that the South African referees have been giving away a lot of yellow cards.
"We talked a lot about being disciplined, and we expect that consistency throughout the whole game."
Umaga did concede that questions would be asked of SANZAAR regarding some of the questionable calls made by van Heerden.
"Obviously I've got to go through the right channels in terms of reporting back with any issues with the referee, which is what we'll do, making sure we get answers for some of the questions we have," he said.
Umaga also commented on the injury of Piers Francis, who came off the field amid concussions concerns.
"He's good actually, he was a bit disappointed he came off.
"I spoke with him about 10 minutes ago and he was talking to me about why he came off and he felt fine, but he wasn't - that's what you'd expect from a competitor like Piers.
"We made the right call bringing him off, because I definitely think he was concussed and we just need to make sure that now he follows the right protocols in trying to get back and play when he can."
Despite encouraging progress since the conclusion of the game, Umaga said that Francis failed the concussion test immediately after it became apparent that he was knocked unconscious.
With Francis and Ihaia West both injured, the Blues' leading two first five eighth's are now unavailable, meaning Umaga will be forced to call upon rookies Bryn Gatland and Stephen Perofeta should Francis or West fail to recover in time for the Chiefs fixture at Eden Park next Friday.
Gatland has looked solid since coming into the Blues squad as an injury replacement, making his Super Rugby debut against the Hurricanes last month.
The North Harbour pivot would probably be the front-runner to start in the 10 jersey against the Chiefs if Francis and West remain unavailable.
The 20-year-old Perofeta has been out of action all season with an ankle injury, but he is a highly touted first-five and could be in line to make his Super Rugby debut next weekend.
"Stephen Perofeta was playing club rugby today, and we haven't heard anything yet," Umaga said.
"Ihaia was making good progress, but we won't know that [who's available to play against the Chiefs] until we get back really, or tomorrow when we have another assessment."