The striker's slight hamstring injury rules him out of tonight's second leg tie against KR Reykjavik, and he joins skipper Scott Brown and winger James Forrest on the sidelines.
The Hoops go into the Murrayfield match leading by just the single goal scored by Callum McGregor in Iceland last week.
Any slip up would see the Scottish champions crash out of Europe for the season.
But manager Ronny Deila is confident that, given the number of chances his side created in Reykjavik, they will have the opportunity to make the game safe and line up a third-round clash with either St Pat's or Legia Warsaw.
And, Deila believes that, with Kris Commons set to recover from his dead leg and start the match, and with Teemu Pukki in good scoring form, plus Leigh Griffiths and Tony Watt ready to shoot on sight, he has enough in his armoury to finish off the Icelanders.
As he prepared to send his players out on to a Murrayfield pitch which he admits looks so good he'd like to pull his boots back on himself, the Norwegian said: "We are going to attack, as we did in Iceland. I think we have strikers who can hit the target.
"So, if we can continue creating so many chances, eventually we will have a lot of goals as well. In Iceland, I was very happy with the second half when we created a lot. In the first half, it was too much sideways.
"This is a very important match and we want to have 90 minutes like the last 45 we had in Iceland with good pressure, more penetration and more runs forward."
Deila is sticking to his mantra it is not just about winning, but also about how his team wins, insisting performances are up to the standard he always demands.
However, he is not blinded to the fact that, in these pivotal games, winning is essential. And, even with Stokes out of action, he is heartened by the array of attacking players he has who can be slotted into his offensive style.
"Anthony is not in the squad because he has a little injury," he explained. "It's a pulled muscle in his thigh. It's nothing big, but we don't take any chances with that. Later this week he will be fit again."
Deila continued: "We have so many strikers in the squad. We have Pukki, of course, and Leigh Griffiths can play there.
"Tony Watt is in the squad as well. He has special skills and something extra. So, we have options there."
Most heartening of all, however, is the news that Commons has shaken off the thigh knock he took after scoring Celtic's goal in Saturday's 1-1 draw in Dresden.
"Kris trained by himself yesterday, but he will be okay," said Deila, who expects Reykjavik to pose them more problems than in the first leg.
"They will be even better," he said. "So it will be about us and what we do with the ball."