The Hoops star insisted they were not going to settle for a point in the Luzhniki Stadium – even when they were trailing 2-1. The defender said: "We looked at the first two games in the group and knew there were points in them for us. We have managed to pick up four, and we are delighted with that.
"Now we have two massive matches, but that's why we are in this competition.
"We are looking forward to them, and we will not fear anyone."
Mulgrew is still coming to terms with the fact the club have finally delivered their first Champions League group stage away win at the 19th attempt.
But he does not accept that is the record of this present side, and believes they can use this victory as a platform on which to build their own history.
He said: "This team made history, and now we can just look forward."
Mulgrew explained that the constant references to the club's poor away record in Europe was not a burden to the current crop of players.
He said: "To be honest it was never a big talking point among us. This is a whole new team now, almost, and it is not our record.
"We are delighted with this victory. This group of players' away record is decent, and we just want to get more points in this group."
The confidence levels have been boosted by the manner of last night's victory, coming back from 2-1 down after having taken an early lead.
Mulgrew revealed there was never any panic, just sheer determination and said: "Everbody believed, but we knew we had to get on the ball more and make things happen.
"We managed to do that, and then there was the sending off, and we kicked on from there."
Mulgrew was shocked when, initially, the referee refused to call the foul by Juan Insaurralde on Gary Hooper as he burst through, and is grateful that one of his assistants persuaded him to change his decision.
"He definitely had not given it, but I think the assistant on the side did," said Mulgrew, who had already been booked for contesting a decision in the first half.
"It was blatant. He got it right in the end, and it did make a big difference playing against 10 men.
"We got on the ball a bit more. But the belief was always there."