The 18-year-old Verstappen became Formula One's youngest race winner at Sunday's Spanish Grand Prix, with Australian Ricciardo finishing fourth after a strategy error by the team was compounded by a late puncture.
Ricciardo, winner of three races in 2014 when, like Verstappen, he moved up from Toro Rosso to the main Red Bull team, had led after Mercedes pair Nico Rosberg and Lewis Hamilton collided on the opening lap.
"The critical point now is what will happen with Ricciardo," Villeneuve, who took pole and almost won on his race debut with Williams in 1996 as a fresh young team mate to Britain's Damon Hill, told reporters.
"Right now it's the reverse situation of when he arrived (at Red Bull) and (Sebastian) Vettel was the driver, except Vettel had four world championships and he doesn't.
"His smile will not carry him now," added the Canadian.
Red Bull put Ricciardo, who had led for 31 laps, on a three-stop strategy at the Circuit de Catalunya while keeping Verstappen on what turned out to be a winning two.
The Australian, famed for having the biggest smile in the sport, said after the race he felt victory had been snatched away from him.
"It's not hard to see Max on the podium but it's hard for me not to be on the podium, that's the biggest disappointment," he said.
"It didn't make sense," he added of the decision to switch to a three-stop strategy after Ferrari had done so with Vettel. "It's frustrating, I think we just threw the win away.
"Sure I'm bitter right now. Not with Max, not at all, just bitter at the situation."
Red Bull principal Christian Horner, who saw "uncanny" similarities between Verstappen and a young Vettel, said the Dutch youngster would only grow in confidence but also offered words of support to Ricciardo.
"At that point in the race it was far from obvious which was the quicker route to go and we felt Vettel, as the biggest opponent, we would take him on with Ricciardo," he said of the strategy.
"I said it before the weekend and I really believe we've got the strongest pairing of drivers in Formula One now," added Horner. "We're in a position where things are on the up."
(Editing by Peter Rutherford)
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