Hoops defender Charlie Mulgrew was sent off for deliberate handball on the line in the 66th minute before Daley Blind scored from the resultant spot-kick but the damage had been done long before then.
Neil Lennon’s men were given the runaround in a one-sided first-half which ended with the visitors three goals down.
In the 13th minute Ajax midfielder Siem De Jong drove into the top corner from outside the box giving Parkhead keeper Fraser Forster no chance.
The Dutch side were a class apart but Celtic did not help their cause with some slack defending, which cost them dearly in the 21st minute when striker Kolbeinn Sigthorsson tapped the ball into the empty net to make it 2-0.
The visitors looked flat-footed in comparison to slick and pacy Ajax who were in total control, keeping the ball for long spells and threatening any time they approached the Celtic box.
However, when the home side grabbed number three in the 27th minute, moments after De Jong curled a free-kick from 25 yards just past the post, they only had themselves to blame again.
In one of his more casual moments stopper Thomas Rogne got himself caught in possession, allowing Thulani Serero to run through and slide the ball under Forster.
Celtic improved marginally after the break but on the hour mark Forster had to make a good close-range block save from Viktor Fischer who had been set up Sigthorsson in another swift Ajax break.
Mulgrew’s indiscretion came when, with the Parkhead defence all over the place, he instinctively put his hand up on the line to save a Fischer shot but it was all in vain as Blind slammed the penalty past Forster.
Moments later the impressive Jody Lukoki let himself down when he failed to hit the target when he was through against Forster.
A multitude of substitutions for the final 15 minutes did no more than give those players a run-out and the game petered out with Lennon left to try to find some positives ahead of the friendly against Norwich at Celtic Park on Tuesday.