Celtic boss Neil Lennon fumed as he saw his side lose 4-2 at Rangers after leading 2-1 at half-time. "I am angry, full stop, with our overall performance," he said.
"I wouldn't like to question their character but I had to ask that after the game.
"I don't know if there was any fatigue from the game on Thursday night (against Atletico Madrid) night but we were second best a lot of the time and in games of this calibre you have to be physical, you have to win second balls, you have to battle and scrap and there was not a lot of that on show in the second half.
"We didn't compete and it was almost as if the players went out for the second half thinking the game was already won.
"I am certainly disappointed with the second goal from the corner," the former Celtic skipper added.
"It was reminiscent of the one we lost on Thursday night, it was almost a carbon copy and it is people not doing their jobs properly and that has cost us the game.
"You have to earn the right to play in these games and we did that in the first half and got a foothold in the game and got a bit of luck with our second goal.
"But we competed and defensively I didn't see our goalkeeper having much to do.
"The warning signs were there when Davis hit the bar at the start of the second half but we didn't take any heed and we lost the physical battle.
"We had given them all the instructions that they might have had to weather a bit of a storm which is what you have to do sometimes but we looked flat in the second half and that is not like us."
For Mulgrew's dismissal, Lennon said: "I actually didn't think it was a sending off, I thought he got plenty of the ball so I was a bit annoyed about that."
