The Bhoys were beaten 2-1 in Benfica on Tuesday night, but know that if they better the Portuguese team's result in Barcelona on matchday six they will join the Catalan giants in the last 16.
However, former Hoops midfielder Collins was disappointed by Neil Lennon's men's composure on the ball at the Stadium of Light, and fears they could come unstuck if they are similarly sloppy at home to Spartak, who are certain to finish bottom of Group G.
"The Celtic fans will be singing from the first whistle to the last which will give the players energy, while hopefully James Forrest, an active little winger, will be back," Collins told Sky Sports.
"Spartak are out so they might come nice and relaxed, but you have to fancy Celtic at home as they have great endeavour and spirit and are good defensively. If they put in a performance they will win, but they will need to work harder on retaining the ball."
On the Hoops' defeat in Lisbon, Collins added: "Celtic never really started against Benfica and kept giving the ball away cheaply and if you do that at this level eventually you are going to get punished.
"They huffed and puffed and tried to get back in the game, but there were poor passing choices and a lack of calmness. I thought it was their poorest performance in the group so far."
Bhoys midfielder Victor Wanyama will be suspended for the crucial clash with Spartak, after picking up his third booking of the Champions League campaign in the dying minutes in Portugal.
Sky Sports pundit Ray Wilkins believes the 21-year-old will be a huge miss for Lennon's side, and wonders if the Hoops chief regrets not withdrawing the former Beerschot star earlier in the contest.
"I didn't realise until this game how influential Wanyama was for Celtic and I think they have got a really tough game coming up now (with him banned)," said the one-time Chelsea man.
"Wanyama got the booking in the 85th minute and Celtic were not really pressing forward at that point, while when you are getting tired in a game like this and you are playing against nimble-footed footballers there is every chance you might make contact.
"Neil might look back and think: 'Should I have taken him off and put someone else on just to save him for this massive game (against Spartak)?'.
"It is a tough one as you still hope you can get the equaliser, but they had played the whole of the second half not looking like they would get back in it.
"The saving grace for Celtic is that Spartak were taken to task by Barcelona on their home soil - or home plastic, should I say - on Tuesday and Barcelona looked unbelievable. Plus, I didn't see anything in this Benfica team to tell me they are capable of getting a point at the Camp Nou."