But it doesn't need to mean crashing out of the race for a Champions League group stage place - even if they trail Legia Warsaw 4-1 in their qualifier.
Callum McGregor - who scored the Hoops' goal in Warsaw before they shipped four to leave qualification hope hanging by a thread - believes the absence of the injured Brown was a major factor in the midweek horror show.
The skipper's torn hamstring will put him out for the rest of the qualification campaign, whether it is for the Champions League or Europa League.
So the Hoops will have to fill the void his absence has created and pull together behind deputy Charlie Mulgrew to stop their Champions League dreams dissolving.
McGregor, 21, believes Brown's importance is not recognised until he is absent. "We really missed him on Wednesday," he said. "He is an unbelievable leader.
"And when things go against you he is one, along with some others, who really galvanises the team and keeps us together."
Despite remaining in rehab and not being set to return to action until late September, Brown will work behind the scenes to pick up his team-mates ahead of the return tie at Murrayfield.
But even he struggled to find anything to say after the Legia lashing. McGregor revealed: "After the game, the dressing room was silent. I have never known anything like that.
"The Champions League means everything to Celtic, and, to suffer defeat like that is so hard to take.
"But we have got a lot of strong characters in our squad, and we will be ready for the second leg."
His away goal could yet prove vital to the Hoops. McGregor added: "It was just a pity we couldn't hold onto our lead for a bit longer.
"If we had managed to do that, then the game might have been different."
The reality is that Celtic not only require to win by at least three goals at Murrayfield, but will have to do so without Brown and now the suspended Ambrose.