Christopher Jullien admits he felt pain for Celtic's stalwarts after Hoops fans turned up at Parkhead to vent their fury following the Betfred Cup defeat by Ross County on Sunday.
Hundreds of supporters demanded the removal of boss Neil Lennon, amid scenes of chaos as police tried to keep order.
The Glasgow club released a condemnatory statement, part of which focused on the players' exit from the ground and which read "to require an escort from Celtic Park while being targeted with missiles, is simply unacceptable".
It was Celtic's first domestic cup tie defeat in 36 and it came after they were knocked out of the Europa League last month.
The Hoops can secure an unprecedented quadruple domestic treble when they play Hearts in the William Hill Scottish Cup final on December 20.
But they have won just two of their last 10 matches in all competitions and sit 11 points behind Rangers at the top of the Premiership, albeit with two games in hand, as they bid for their 10th successive title.
Ahead of a Europa League dead rubber against AC Milan on Thursday night, Jullien, who signed for Celtic from Toulouse in June 2019, said: "I have been here one year, I know that the club wants to win so much.
"It hurts me a little but I feel pain when I watch Broony (Scott Brown) on my right and see Callum (McGregor) on my left, or Tom (Rogic) or James (Forrest) the next morning because these players keep giving everything for this club.
"They have been workers and I can't talk about what they have achieved, it has been huge. I feel hurt for them.
"We are going to do everything to achieve our goal this year.
"My message (to fans) is probably, we can't win championships in November or December. We can win championships in May, June.
"It is hard to accept defeat. After every loss I am going home, I am hurt, I can't sleep, it is difficult but at the end of the day the championship is a marathon, it is not one game."
