Sunday's resounding 4-0 victory over St Mirren saw Celtic extend their unbeaten league record this season to 20 games and stretch their lead at the Scottish Premiership summit to 13 points.
It became eight clean sheets in a row in domestic competition in Paisley and Ambrose told this week's Celtic View: "It's satisfying and we're trying our best to see how long we can keep it going.
"It won't be easy but every day we have to improve and do better in each game we play. We are still trying to do this not only in defence but in every area of the pitch."
And the defender is adamant that the back-line aren't solely responsible for keeping the opposition at bay.
"It's not only down to the defence but it's down to the team - they have kept eight clean sheets, not just the defence," he explained.
The big victory over the Buddies was the perfect way for the Hoops to enter their short winter break which saw Neil Lennon's men head to Turkey to participate in a four-team tournament involving Ajax, Galatasaray and Trabzonspor over the course of seven days.
Ambrose is confident the trip will prove a useful exercise giving the Scottish champions another chance of silverware.
"He is the boss and we will do what he wants, and sometimes he is like a father to some of us as he has helped us with so many things," added the Nigeria defender.
"But we are not going to just relax, as we're going to take part in this tournament and we want to achieve something there," he added. "I think we are going there to prove a point.
"After going out the Champions League, winning that tournament would be very good for us."