The Bhoys took the lead through Nir Bitton, before Viktor Fischer equalised for Ajax in the first half, though Mikael Lustig put Celtic back in front just before half time.
Defender Emilio Izaguirre was sent off for Celtic, and Ajax took advantage by notching a late equaliser through Lasse Schone.
The Amsterdam giants couldn't find a winner, with Celtic defending valiantly with ten men to preserve the point they worked hard for.
However, those defensive tactics didn't go down well with Ajax manager Frank de Boer, who told Four Four Two after the game that it was difficult to play against a team who 'parked two buses' in front of the goal.
"It’s always difficult. They parked two buses in front of us," said De Boer. "It was a bit of a false start for us with the early goal for Celtic. The spaces were small and tight. We had great difficulty, but we scored a great goal. It’s disappointing when you control the game, but then they score another goal.
Any team would pack men behind the ball following a red card, and Celtic were no different in that respect as they earned a valuable point.
After questions had been asked about Celtic's defence, manager Ronny Deila will be happy to have seen his side dig in and battle for a point, with new signing Jozo Simunovic enjoying a fine debut in the Celtic back line.