The Wire were beaten 26-22 at Leeds Rhinos but as they tried to fight back late on, the sight of Tanginoa limping from the field in back play was another blow for the visitors.
Prop Luke Yates was also withdrawn late on and while Burgess believes the news on him is better, he says Tanginoa’s condition is more of a concern.
“We don’t know the full extent of it but it looks like a bit of a groin issue,” he said.
“He’s not looking too healthy but we’ll figure out how bad it is over the next few days.”
On Yates, he added: “Yates had a bit of a stinger and we were at a point in the game where we couldn’t really have any passengers.
“We had enough substitutions up our sleeves so we sent Jordy Crowther out there, but I think he’ll be okay.”
Warrington only used 16 players at Headingley, with young outside-back Lachlan Webster an unused substitute having been named on the bench as part of an unchanged 17.
When asked whether he would have made a different decision about his selection with hindsight, however, Burgess insisted he felt the call he had made was right at the time.
“Sometimes, we carry that spare interchange player and we had a couple of niggles in the outside-backs,” he said.
“If it comes off, you look smart and if it doesn’t, you get asked questions like these.
“It was the right decision for the team, but it was unfortunate for Lachie.
“I don’t like doing that to players, but we couldn’t find space for him.”