Edson Alvarez, Steven Berghuis, Mohammed Kudus and Steven Bergwijn were on target for the Dutch champions as they shrugged off the loss of a number of key players in the transfer window.
Rangers' run to the Europa League final last season and victory over Ajax's Eredivisie title rivals PSV Eindhoven in qualifying for the group stage raised hopes Giovanni van Bronckhorst's men could compete in a group also containing Liverpool and Napoli.
But after losing 4-0 to Celtic on Saturday, Rangers were blown away before half-time for the second time in a week.
"We knew the Champions League would be a high level and Ajax showed today throughout the game how good they are, how strong they are," added Van Bronckhorst. "You have to be 100 percent ready for the game."
"We have to compete with the squad we have and are able and capable of making. We knew it was going to be tough and it showed today.
"To compete in the Champions League you spend hundreds of millions, for us to compete it is too much to ask," said Van Bronckhorst, whose summer signings amounted to just over £10 million ($12 million).
Ajax brought in over 200 million euros ($199 million) in transfer fees for Antony, Lisandro Martinez, Sebastien Haller and Ryan Gravenberch in recent months.
However, they withstood interest in Alvarez late in the window from Chelsea and the Mexican opened the floodgates when he was left unmarked to head in a corner on 17 minutes.
Ajax look to have reinvested their transfer income wisely, including the signing of Calvin Bassey from Rangers.
The Nigerian international has been badly missed at the heart of Van Bronckhorst's defence in the opening weeks of the season.
James Sands has deputised at the back due to a number of injuries at centre-back and it was the American international who deflected Berghuis' shot into his own net to double Ajax's lead.
Just like at Celtic Park at the weekend a two-goal deficit quickly became three for Rangers when Kudus's storming run found the finish to match as he smashed in off the far post.
Van Bronckhorst responded with three substitutions at half-time and a change of system which held stem the flow of Ajax attacks.
However, Rangers were still undone by another self-inflicted blow for the fourth when Bergwijn latched onto Ryan Jack's slack pass to round Jon McLaughlin and slot into an unguarded net for his eighth goal in seven games since returning to the Netherlands from Tottenham.
