The Parkhead side's 1-0 win over St Mirren on Sunday was the 11th game in a row in which England stopper Forster was not beaten.
That tally bettered the club's previous record of 10 clean sheets set twice - first in season 1913/14 and then again eight years later.
But Ambrose says the club's outfield players deserve their share of the credit too.
The Nigerian international told the Celtic View: "The clean sheets are coming not just because of the defence but the whole team, from Fraser to the strikers, because we have been playing as a unit.
"So this is down to the solid work of the team , the instructions the gaffer has been passing on to us and our style of play.
"I believe this is what has been helping the team so far.
"Fraser, Darnell (Fisher), Mika (Lustig), Adam (Matthews), Emilio (Izaguirre), Virgil (van Dijk), myself, the two midfielders, who are important to the defence, and the attackers - everyone deserves credit as it's a team thing, not just the defence.
"We also should give credit to the gaffer and the supporters as they have been solidly behind us."