The Dutch giants lost to the Bhoys when last they met in the Champions League but their coach is certain that they will give a better account of themselves at home on Wednesday
The Dutch champions are on a poor run of form and currently sit bottom of Champions League Group H with just one point from their opening three games but the former Netherlands international feels that they have a good chance of victory in their return clash at the Amsterdam ArenA on Wednesday.
"I think we showed last time that we aren't a worse side than them," De Boer said at a press conference.
"This time we have our fans supporting us and we do have a good chance of winning but maybe it will be even closer than at Celtic.
"We aren't taking enough points at the moment - Ajax and the fans are used to taking three points, so of course people are disappointed.
"Many good things are happening at Ajax but, ultimately, it is all about results and they can be improved. I think we're heading in the right direction but we need to get more points."
Scotland boss Gordon Strachan claimed that Ajax were like a team of "rookies" in the wake of the Parkhead match but De Boer refused to wade into an argument.
"It's a nice expression from him but it's said in a certain context and now everybody takes it seriously," he mused. "Celtic can have a lot of confidence because they had some good results in the past years, even against Barcelona."