The former Celtic and Republic of Ireland goalkeeper expects that the game will have taken as much mentally out of the Celtic players as it did physically.
Last season, Celtic's performance levels dipped in the aftermath of the European games when they returned to the more routine matters of the league and Bonner believes that the best way to keep the momentum going is to freshen things up a little.
Derk Boerrigter and Teemu Pukki came on for the latter stages of Wednesday night's game, but the ex-Parkhead No.1 expects that more game time from them might enable goals to be more evenly spread throughout the team.
"This is the time when you need to see if the fringe players can step up to the mark," said Bonner. "At the minute the majority of the responsibility for goals is falling onto Anthony Stokes and you do need to have that weight shared out.
"I don't think there will be any complacency with regards to the league, either. At the minute Inverness are doing very well and when you are at a club like Celtic, it is all about results.
"No-one wants to lose ground or be on the back of two successive defeats. The players will be looking to get themselves back on track against St Johnstone and to keep things going in the league.
"You may well find that there is a reaction from Wednesday's game in that it takes it out of you physically as well as mentally, but that's the reason why there is such a big squad at the club - so that the demands of playing in various competitions can be met.
"Today should give some of the players the chance to come in and show what they have got. We've not seen much yet from the likes of Amido Balde and these are the games where they should be looking to come in and make an impression."
Despite the disappointment of losing two late goals in the San Siro, Bonner believes that Neil Lennon will be able to draw out the positives of the display.
For large chunks of the game Celtic made AC Milan look very ordinary, albeit that the Italian giants were without a number of key players through injury.
The goals allowed the scoreline to flatter AC Milan, but Bonner has not discounted Celtic being able to bounce back as the group progresses.
Barcelona are in Glasgow a week on Tuesday and although Lennon's side performed heroics against the Catalan giants last season, it is a tough ask to expect the same again.
While the next week or so will be consumed with domestic business as the SPFL and League Cup fixtures take precedence, Lennon will also be attempting to plot a way past the La Liga outfit.
Bonner said: "You know that on their day Barca can wipe the floor with anyone.
"The fear is that you could be left with nothing after the opening two games which would make it very difficult. But at the same time, I think that although the scoreline from Milan was a sore one, the performance should have given the players a lot of belief.
"They looked very comfortable at that level, although there was a lack of a cutting edge up front where they could have done with a little bit more in the final third. But overall they acquitted themselves well and that has to give them hope going forward.
"They lost two very unfortunate goals. It is a case of trying to pick themselves up now and get going again before getting their minds on the game against Barcelona."
Given the manner in which Fraser Forster was caught out by the deflection from Emilio Izaguirre on Wednesday night and then managed to get a hand to Mario Balotelli's free-kick before being beaten by the rebound, Bonner felt a degree of sympathy for the keeper.
"He could consider himself quite unlucky," he said. "The free-kick was inside his post which makes it an awkward one, as was the deflected shot. It was just one of those nights, really.
"He really proved himself at this level last season and I am sure that he will want to maintain that standard in this competition again.
"Certainly, he can expect to be pretty busy when Barcelona are in Glasgow next month."