The Scottish Premiership side are two rounds away from reaching the group-stages of the competition.
Celtic manager Brendan Rodgers
Brendan Rodgers' men travel to take on the champions of Kazakhstan in the first-leg of their third qualifying round clash on Wednesday after they saw off Lincoln Red Imps in the previous round.
Patrick Roberts scored the third goal for Celtic against Lincoln
But despite the huge levels of optimism that followed the Northern Irishman's appointment at Parkhead as many fans anticipated that he would be the man to lead them back to the group-stages, Sutton has outlined why he is concerned that this next hurdle may be just a little too big for the Bhoys to clear.
"FC Astana qualified for the group stages of the Champions League last season," he told the Record.
"They played three matches at home in their section against Benfica, Atletico Madrid and Galatasaray and didn't lose one of them.
Celtic struggled in Europe last year
"Celtic didn't make the group stages. Instead, they ended up in the group stages of the Europa League.
"They couldn't win a game. At home or away."
While Rodgers would have undoubtedly preferred to have beaten Lincoln in his first game in charge, the defeat may now actually have a positive impact on the side's hopes of progress.
Had they got through as comfortably as many expected, Celtic may have gone into this tie with the same level of complacency that cost them in Gibraltar. And while there was a big enough gulf between the two teams for the Hoops to turn it around in the second-leg against Lincoln, the gap between themselves and Astana is arguably close enough that there may be no way back if they get ahead of themselves.
But with the shock defeat reminding them what can happen, they will surely travel to Kazakhstan feeling that only an excellent performance will keep their group-stage dream alive.