The Australian was dropped for the flagging Wolves' defeat to Wigan last week and was again absent as Burgess's side ended a three-game losing streak with a laboured 30-22 comeback win over Catalans Dragons on Thursday.
Wolves coach Burgess publicly challenged Dufty to "fix his behaviour up" after missing a recovery session and while he has seen encouraging signs since, the 29-year-old's next outing will be in the reserves.
He will be joined by centre Toby King, who was also dropped after a series of disappointing performances amid a run which saw Warrington all but drop out of play-off contention in the Super League.
"He (Dufty) has got to show me he wants to play for this club and play up to our standards, so they will both (Dufty and King) play reserve-grade this week," Burgess, the former South Sydney star an ex-Rabbitohs assistant coach, said.
"I love Matt, he is one of my great friends. We all know what he can bring, he is a brilliant player.
"If he gets a good performance out on Saturday, more than likely we will see him back in the side next week.
"I've challenged him, and it's been a bit embarrassing for him.
"Nobody believes in him more than me but we have standards here and he just missed them."
Warrington's recent woes looked like continuing as they conceded four tries in the opening half-hour - three to former St Helens winger Tommy Makinson - to fall 22-6 behind and suffer boos from home fans.
But they rallied with two tries from Jake Thewlis, the second a spectacular diving effort, either side of a Sam Stone effort. Josh Thewlis made victory certain late on.
Burgess added: "The first half was not acceptable, not up to standard. I was relatively calm (at halftime) considering the performance. I knew if we got our game together we could still win.
"We competed harder, no doubt. The play-offs are out of our hands but we'll look to improve our performance and wherever it takes us, it takes us."
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