The Scottish champions paid the price for some slack defending at the Astana Arena, as well as being guilty of missing some decent opportunities.
And while the robust Kazakhstan side looked limited in many aspects of their play, a dramatic turnaround in front of what is sure to be a packed house is required if Neil Lennon’s side are to reach the lucrative group stages of the competition for the second successive season.
As a result, Mulgrew is hoping the crowd will play their part in the Hoops’ rescue mission.
The Scotland international said: “The crowd will get right behind us and we will really need to go for them. We were disappointed to lose but we are staying positive and looking towards the second leg.
“It was a tough game but we have to believe in ourselves for the second game. We were well prepared, we knew what was coming and we know what we will get again next week but we have to stand up to it better and score a few goals.”
The defeat comes after a summer of upheaval at the Hoops with midfielder Victor Wanyama, striker Gary Hooper and defender Kelvin Wilson all leaving.
In response Lennon has signed Amido Balde, Virgil van Dijk, Derk Boerrigter and Steven Mouyokolo, but his side is clearly still gelling.
Mulgrew added: “We are not using that as an excuse. We knew these questions would come but we have a lot of belief in each other, we have a big squad and enough players to deal with the challenge.
“We have to look at the positives and we have a real chance if we approach it positively next week.
“We knew this tie was over two legs and we are looking to next week to turn it around.”