Mulgrew delivered his upbeat hopes of qualification despite the two devastating late goals which sent them to defeat against AC Milan in last night's Group H opener.
The defender said: "Qualification is still there for us. We'll never stop believing until it's mathematically impossible.
"The manager will keep us going and have us going out there to win games so it's only one game in, there's still a long way to go. I am sure the manager will have a couple of different systems for whatever the occasion is and it's up to him. We just need to do our jobs and fill in where the manager wants us."
Milan's win in the San Siro and Barcelona's 4-0 rout of Ajax in the other Group H fixture means the table already looks split between the two heavyweights likely to qualify and the Dutch and Scottish champions left to contest third place and the consolation of a drop into the Europa League.
Celtic reached the last 16 event after losing their opening group games in 2006 and 2007, though, and Mulgrew said that because anything they took last night would have been a bonus there was no need to write off their chances of making it through again.
"This doesn't change the group," said the
Scotland star. "We just have to focus on every game as it comes and look to win and pick up as many points as we can.
"Barcelona beating Ajax 4-0 means nothing
to us. We have Barcelona next and we know what they possess. We just have to prepare for them.
"There's a lot of belief in that dressing room. We just need to now believe we will get a goal when we create chances."
Mulgrew and captain Scott Brown had helped protect Celtic's back four and it was on the brink of delivering a clean sheet and a point until a Cristian Zapata shot deflected off Emilio Izaguirre into the net eight minutes from time.
With only four minutes left Fraser Forster did well to save a Mario Balotelli free-kick, but could only parry it back into the six-yard box where Sulley Muntari pounced to score again.
"It was really cruel," said Mulgrew. "We felt comfortable.
"But we need to learn that we can't give away goals. There was a bit of fortune with the first one. But we need to look at
the next game and stay positive.
"Every game will be different in this group and it's going to be even more difficult when they come to Parkhead."