On Saturday (AEDT), less than two hours before kick-off, the three-time winner refused to play the match at Parc y Scarlets after claiming COVID-19 "sanitary conditions were not met".
A member of the host's squad tested positive for the virus after last weekend's trip to Bath and the player was put in self-isolation.
He was not picked for the meeting with Patrice Collazo's away side.
"EPCR (European Professional Club Rugby) didn't arbitrate, during the week before the match, the health situation connected to the meeting with the two clubs and only did so some hours before the meeting," a Toulon statement read.
"It forced us into a harrowing decision.
"Toulon considers the decision taken by EPCR as irregular and are studying all possibilities of an appeal."
Tournament organiser European Professional Club Rugby (EPCR) said the Top 14 side had refused the chance to play the match later in the weekend.
The victory takes the Welsh region up to fourth in Pool A and gives the French club a mountain to climb to reach the quarter-finals with just two group games to play.
Three other games had already been cancelled this weekend with Lyon, La Rochelle and Toulouse awarded 28-0 victories against Glasgow Warriors, Bath and holders Exeter Chiefs respectively.
Two matches in the second-tier European Challenge Cup were also called off as Agen and Cardiff Blues were handed wins over Treviso and Stade Francais for the same reason as the cancelled fixtures in the Champions Cup.