Nantes never looked likely to defend its crown at Stade de France, falling behind within four minutes as centre-back Costa climbed to head Branco van den Boomen's corner home.
Toulouse's dream start continued as it capitalised on another set-piece six minutes later, Stijn Spierings crossing for Costa to nod in from close range after Nantes half-cleared a free-kick.
Nantes almost got one back as Gabriel Suazo denied Mostafa Mohamed with a goal-line clearance, but Toulouse had a third 23 minutes in, Dallinga racing on to Suazo's perfect pass to beat Alban Lafont with a dinked finish.
Any slim hopes of a Nantes comeback were then crushed as Dallinga tapped in his second after Lafont saved from Fares Chaibi, stunning Les Canaris' supporters into silence.
Nantes captain Ludovic Blas got one back from the penalty spot when Rasmus Nicolaisen scythed down Fabien Centonze with 15 minutes remaining, but Zakaria Aboukhlal swiftly blasted into the top-left corner to round off the scoring for Toulouse as Nantes's defence crumbled one more time.
While Toulouse can celebrate lifting a first major trophy since predecessors Toulouse FC won this competition in 1957, Nantes must recover quickly as it battles to preserve its Ligue 1 status.