Outside centre Suaalii is set to be sidelined for several weeks after injuring his hamstring during the team warm-up for Friday's 59-19 Super Rugby defeat in Sydney.
Coach Dan McKellar said the former rugby league standout, who was replaced by Waratahs debut player George Poolman, would miss several matches.
"I don't know yet but it looked pretty sore. I'd suggest it's not a couple of weeks. I think it's probably longer than that," McKellar said.
"George did some good things tonight but, you know, you're losing a top quality player.
"No doubt it has its impact but we're not sitting here blaming that. We've got to be better than that."
Suaalii, 22, played only seven games last year in his debut season for the Waratahs because of injuries as they missed the play-offs for a second straight season.
Having opened their campaign with big wins over the Queensland Reds and Fijian Drua, McKellar described their latest performance as "incredibly disappointing".
He criticised his team's high rate of turnovers and missed tackles against the ruthless New Zealand side, who scored nine tries, including a hat-trick to All Blacks midfield back Billy Proctor.
"We spoke about the 2026 Waratahs, and that's not us," McKellar said.
"That's not how we're going to play and that that's not going to define our season."
The Waratahs play their first match on the road next week, against the Queensland Reds.
The Hurricanes, who boast the same 2-1 record as the Waratahs, will host the Western Force.