Brendan Rodgers’s side suffered a 3-1 defeat at the hands of Salzburg in Group B, with James Forrest sent off for the visiting team in the second half.
Celtic legend Bonner was following the match, and the former Republic of Ireland international goalkeeper has given his take on the defeat for the Hoops.
Bonner has also criticised the performance of 31-year-old Sweden international right-back Mikael Lustig.
Meanwhile, Celtic manager Rodgers has praised 20-year-old forward Odsonne Edouard for his goal against Salzburg.
Bonner told BBC Sport (19:43): “Celtic changed their midfield structure and it's taken away from their defensive set-up and they've been undone with it.”
“I was hoping we would get to the end of the game and not have to talk about Mikael Lustig stepping out of defence and making a square pass and giving it away in a bad area - but he has done,” added Bonner.
“I was also going to talk about the defensive structure, but they've restructured it and it’s fallen down.”
Rodgers told The Scottish Sun: “Our plan in terms of being compact and being able to threaten on attack, it worked well for us and we had a great start. Odsonne showed his pace, strength and a finish.”
Over the course of the 90 minutes on Thursday evening, hosts Salzburg had 65% of the possession, took 25 shots of which six were on target, and earned seven corners, according to BBC Sport.
Visitors Celtic had 35% of the possession, took four shots of which two were on target, and earned two corners, according to BBC Sport.