The Dutch giant lost to the Bhoys a fortnight ago but the club's coach is certain that it will give a better account on home soil on Wednesday.
The Dutch champion is on a poor run of form and currently sits bottom of Champions League Group H, with just one point from the opening three games.
However, the former Netherlands international believes the club has a good chance of victory in the return clash with Celtic 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 was like a team of "rookies" in the wake of the Parkhead 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."