With just one point from their opening three Champions League matches, their hopes of reaching the latter stages of the competition appear forlorn, but the Dutch side remain adamant that a victory against Neil Lennon's side can still revive their chances.
Confidence was not a casualty of the loss at Celtic Park because the Ajax players were heartened by the chances they created. Christian Poulsen hit the post with a volley, Thulani Serero was twice through on goal, while Kolbeinn Sigthorsson shot wide from the edge of the area.
"A draw was more [fair] when you see the chances we had," said full-back Daley Blind. "They were a little bit lucky. We are confident, we have a team with a lot of trust, we believe in ourselves and at home it can be a nice game. We play good football and if we take some moments in the game to put Celtic under pressure, we can come out of it. That's how we want to play and make chances."
The Ajax players dwelled upon the positive aspects of their performance but their own defensive flaws, and their inability to cope with the surging momentum that Celtic were capable of, resulted in their defeat.
The centre-back pairing of Joel Veltman, a 20-year-old making his European debut, and Stefano Denswil, a 21-year-old with very little first-team experience, was vulnerable throughout. Denswil was rash in the way he lunged at Anthony Stokes to concede a penalty, and he inadvertently contributed to the second goal by deflecting Biram Kayal's shot past Jesper Cillessen. None the less, the youngster was unbowed, accusing Stokes of going "down very easily".
The defeat confirmed Ajax's unwanted statistic of having failed to win an away fixture either domestically or in Europe, but that was of secondary concern to Poulsen who took heart from the manner of the performance.
"Against Celtic, we had good possession, created chances and then we couldn't score," admitted the former Liverpool midfielder. "Celtic came at us strongly in the first 10 minutes, but after that we controlled the game and got our passing going.
"Now it is looking difficult to get through this group. For us and Celtic third place in this group would be good, but now we really need to win the next game and see what happens.
"For the most part, we did well. We got through by playing well with our small technical players and we played between the lines of the Celtic team. Putting the ball into the goal was the only problem. So far this season we haven't lost at home and we feel comfortable at home. We will respect Celtic, but we have our own fans in Amsterdam and that will help us."