Gers were back in the competition for the first time in 12 years as they took to the Johan Cruijff ArenA in Amsterdam, but it was the Dutch side who took control of this opening Group A match.
Giovanni van Bronckhorst named one change from the weekend's Old Firm with Scott Wright coming in in place of Steven Davis.
Rangers lined-up with the same back five of Jon McLaughlin in goal and James Tavernier, Connor Goldson, James Sands and Borna Barisic in front of him.
John Lundstram, Glen Kamara and Malik Tillman were in the middle of the park, with Ryan Kent and Wright in support of Antonio Colak.
The home side were the first to have a sight at goal as Jurrien Timber headed over the bar after getting on the end of a cross from Dusan Tadic, before Steven Bergwign also dragged a shot wide shortly after.
Rangers came close to a break from an Ajax set piece as Antonio Colak did well to set Malik Tillman on a run into the opposing half before he cut the ball back to Colak. His shot was blocked with Ajax able to deal with the danger.
However, it was the home side who got the lead with 17 minutes on the clock. A corner was swung into the box by Steven Berghuis with Edson Alvarez rising to head beyond Jon McLaughlin.
McLaughlin was called into action shortly after and pulled off a good save to deny Devyne Rensch before the right-back had another opportunity for the Dutch side as he was inches wide after quick build-up play from the hosts.
With just over half an hour played in Amsterdam, it was 2-0. Steven Berghuis’ effort from inside the box was deflected off James Sands and into the back of the net.
Minutes later it was 3-0 as Calvin Bassey played the ball forward to Mohammed Kudus, he turned to drive into the box and struck a powerful shot across goal and into the top corner.
With the game approaching half-time, McLaughlin denied Dusan Tadic as he pushed wide an effort from the Ajax captain.
Manager Giovanni van Bronckhorst made three changes to his side at the break with Leon King, Ryan Jack and Rabbi Matondo introduced in place of James Tavernier, Malik Tillman and Scott Wright.
James Sands headed wide from a Borna Barisic free-kick early in the second-half as Rangers searched for some way back into this match.
Ajax came close to adding to their tally with 25 minutes of the match remaining when Mohammed Kudus weaved his way into the box but his final touch took it away from him and Leon King was able to clear the danger.
At the other end, Rabbi Matondo managed to pick out Ryan Kent with a ball from the right but his effort was just wide of the target.
The Light Blues did have the ball in the net in the 71st minute and it was a fantastic strike from Borna Barisic but the goal was disallowed after a VAR check showed Ryan Kent to be offside in the build-up.
It was four for Ajax in the 80th minute as Steven Bergwijn latched onto a loose pass in the Rangers defence to go through on goal and slot low beyond McLaughlin.
Attention for Rangers now turns back to Scottish Premiership action with a trip to Pittodrie to face Aberdeen on Saturday.
RANGERS: McLaughlin, Tavernier (King, 46), Goldson, Sands, Barisic, Lundstram, Kamara (Davis, 77), Tillman (Jack, 46), Kent, Wright (Matondo, 46), Colak. I’ll
Subs: McGregor, McCrorie, Ridvan, Davies, Devine, Arfield, Morelos, Fashion Jr.
Ajax: Pasveer, Timber, Bassey, Alvarez (Sanchez, 88), Bergwijn (Ocampos, 81), Taylor, Tadic, Rensch, Blind (Baas, 81), Kudus (Brobbey, 89), Berghuis (Klaassen, 81).
Subs: Stekelenburg, Gorter, Kaplan, Lucca, Grillitsch, Magallan, Conceicao.
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