Celtic chief executive Peter Lawwell has asked for "strength in adversity" after calls from supporters for manager Neil Lennon to be sacked.
Protests were held outside Celtic Park after a League Cup loss to Ross County.
The nine-in-a-row winners, already out of the Europa League, trail Premiership leaders Rangers by 11 points, albeit with two games in hand.
"This is not about any individual, but about Celtic Football Club as a collective," said Lawwell.
"Neil, the players and backroom staff, who have already done so much for the club, share in all of that. They have never been more determined to succeed. Having enjoyed such sustained, unprecedented success, we now need strength in adversity."
The 2-0 loss to County on Sunday halted a 35-game winning streak in domestic cup competitions, and compounded an already shaky period for Lennon's men.
His side have won just two of their past 10 games in all competitions, with an away trip to AC Milan in the Europa League on Thursday up next.
Despite their League Cup exit, Celtic are just one win away from completing a quadruple treble when they play last season's delayed Scottish Cup final against Hearts on 20 December.
"Together we have faced unique difficulties in the early part of the season," added Lawwell. "While some of these were beyond our control, of course we recognise we must improve. There is a long way to go and everyone at the club is ready for the challenge.
"Later this month, Celtic will attempt what no other club in the world has achieved - a quadruple treble in domestic competitions. We can best prepare for that and for our other remaining competitions this season by moving forward together, with the sole aim of achieving continued success for the club."
Speaking after Sunday's defeat, Lennon conceded the pressure was mounting on him, saying: "There is an expectation at this club, there's a demand for excellence and there's a demand for wins - I am fully aware of that.
"I am not standing here like the happy clapper saying everything's OK, because it's not. But we'll do everything we can - if I've still got the opportunity to do that - to turn things around."