Celtic cannot afford to lose on Thursday and realistically need to win to retain their qualification prospects.
Assistant boss John Collins said after consecutive defeats to Norwegians Molde that they would not change their attacking style for any team.
But Bonner feels Celtic, who drew 2-2 in Amsterdam in their opening group game, can succeed by picking Ajax off at Parkhead.
"The way Ajax will play will always give teams an opportunity," the former Republic of Ireland goalkeeper said.
"They are a young team and a bit brittle at times but they play that typical Dutch/Ajax way of expansive football.
"They are very open and if you can defend well against them, I think you can exploit the space that is left
They will throw their full-backs forward and open up, and I think Celtic can score against that type of team.
"They don't come up against it very often, especially at home, and I think if they can defend well and exploit those opportunities, they have a chance of winning that game
But they have to defend well.
"I've always said in Europe you have to be more cautious
You can't play the normal way Celtic play, especially under Ronny when they push full-backs forward and almost leave it two v one at the back.
"I think you've got to be a bit more adaptable and change it a bit to get a chance."
Bonner was part of a Celtic team that knocked Ajax out of the 1982-83 European Cup with the help of a spectacular Charlie Nicholas strike in Amsterdam and believes another win over the Dutch side could be just as memorable.
"That was a great Ajax team but we were decent ourselves," the 55-year-old said.
"There was a good competition in Scotland at the time: Dundee United, Aberdeen, Rangers, to a point, and ourselves
The fans were happy and Europe was a real bonus to us at that time.
"Those big nights will always go down in history, beating Ajax in Johan Cruyff's last season, nights we talk about still
That's what creates the history and that's what we need on Thursday night also.
"If they can get through the group then everything changes, it would be magnificent
They are top of the league and have a chance in the two cups but these two games coming up are vital."
Bonner was speaking at Hampden's Scottish Football Museum after handing over a rare framed recording of 'The Laddie Frae Cardenden', a song by Glen Daly about former Celtic goalkeeper John Thomson, which was donated by the late Scottish entertainer's family.
Thomson died aged 22 in 1931 after being injured in an Old Firm game in his 188th appearance for Celtic.
Bonner said: "The history of Celtic was huge when I grew up in Donegal
The picture of the European Cup-winning team was up on a wall in the house next door, and the Johnny Thomson story was always there
People talked bout it.
"I remember my uncle living in Glasgow and that was one of the first things I got to know about Celtic, that legend of a story.
"It's lovely to be here commemorating him and talking about him
It's such a long, long time ago but still people talk about him
The younger generation need to know the story.
"And as a goalkeeper, when you go out on the pitch you are almost taking the mantle of people like himself and Ronnie Simpson
That was in the back of your mind."
Source : PA
Source: PA