Ajax, now 283 minutes without scoring a goal in the league, started with Ioannis Anastasiou as central striker but the Greek missed four good chances, while Nigel de Jong saw his injury-time goal disallowed for offside.
Ajax will travel to Swiss side Thun on Wednesday for a Champions League Group B match and are likely to miss Tunisian Hatem Trabelsi, who came off in the first half with a hamstring injury.
Ajax remain fifth with 15 points after 10 matches, seven points behind leaders PSV Eindhoven, who travel to Twente Enschede on Saturday.
AZ Alkmaar are second with 21 points and meet ADO Den Haag, while Feyenoord, also on 21, face Willem II Tilburg on Sunday.
Heerenveen, tenth with 12 points, host CSKA Moscow in a UEFA Cup tie on Thursday.