The Hoops' shock 1-1 William Hill Scottish Cup fourth round draw against Arbroath at Parkhead yesterday means Neil Lennon's men have not won a domestic game in front of their own fans since beating St Johnstone 5-0 in the Scottish Communities League Cup on October 30.
A 1-1 draw against Saints and a 1-0 defeat to Inverness in the Clydesdale Bank Premier League were compounded by failure to beat the Irn-Bru Second Division part-timers.
However, during that period Celtic Park witnessed one of the club's greatest ever wins when the Hoops beat Barcelona 2-1 in the Champions League and in midweek Group G will come to the boil.
The Scottish champions need to do better against Spartak than Benfica do in the Nou Camp in order to secure a last 16 spot and the Nigerian defender believes playing for such high stakes will make a difference.
"Wednesday night is a Champions League game which we know we have to win to get a place in the last 16 because we are not counting on Barcelona to do the job for us," said Ambrose.
"We have to do that at Celtic Park.
"I believe the atmosphere will be different to the one against Arbroath.
"We have been playing well outside Celtic Park and winning games so I don't really know what is going on at home.
"We are all disappointed. It has been quite long now without a (domestic) victory at home.
"I believe the problem is scoring goals at Celtic Park but we will be on it very soon.
"I can't make any promises, we just have to do it.
"We disappointed the fans again yesterday, they came to see us winning at home.
"We had a lot of chances and didn't convert them and as you saw, one goal is not enough to get a victory.
"They got one shot which got a deflection before going in but I suppose that is football."
Celtic fans will certainly see a different side against Spartak to the one which made such heavy work of what should have been a straightforward win over Arbroath.
Neil Lennon made nine changes to his side which beat Hearts 4-0 in the SPL at Tynecastle in midweek, with Ambrose and midfielder Victor Wanyama - suspended for the game against the Russian club - the two survivors.
The SPL leaders dominated from the first whistle but it took an own goal from Alex Keddie in the 35th minute to put them ahead.
Arbroath keeper Scott Morrison helped keep the makeshift home side at bay and with four minutes remaining Steven Doris sent a deflected free-kick from 25 yards past stand-in keeper Lukasz Zaluska to ensure a replay on Wednesday week.
Arbroath player-manager Paul Sheerin claimed his side's result was an even better achievement than when he scored for then First Division Inverness in their famous 3-1 Scottish Cup win at Parkhead in February 2000.
The 38-year-old is looking forward to welcoming Celtic to Gayfield for the replay.
"It is not a nice place, it is cold and windy at times but it is our home and we do well there," he said.
"We pick up good results there and from the club's point of view, financially, it is massive.
"Fingers crossed that the television companies cover it."