The Scottish champions were handed another thrashing on Wednesday night when they lost 5-1 to Real Madrid at the Santiago Bernabeu.
Celtic did do better than Rangers in the Champions League in terms of getting two points, but finished bottom of their group and are out of Europe before winter sets in.
The Bhoys have been accused of being too attacking in the Champions League and Ange Postecoglou has been insistent that he will not compromise on his principles.
However, Bonner stressed that at Champions League level Celtic will continue to get exposed if they do not tweak their game against the best teams.
He insisted that he does not want the Celtic manager to compromise but feels that he needs to recognise that the best teams will put them to the sword if his team do not learn how to stay in games.
“In this competition, you get exposed if you don’t adapt”, the Celtic legend said on BBC Sportsound.
“Nobody is saying he [Postecoglou] has to compromise on his attacking style and building through the thirds from the back.
“But they need to learn how to stay in the game against top opposition.
“Maybe getting the players to think slightly different.
“Instead of taking 80% risk of running forward, maybe they should sit a bit and help their colleague in midfield.
“They play with inverted full-backs not in a defensive role, but more to be in as a player who can get on the ball and take risks.
“They leave themselves slightly exposed.”
Celtic will now focus on retaining their Scottish Premiership title and gaining direct entry into the Champions League again next season.
