Chelsea centre-back Cahill believes that it is a record that Roy Hodgson and the team should take great pleasure from.
"At any stage you could have a free kick, set piece or individual mistake," he told the FA's official website. "That's the thing with only being 1-0 up.
"That can always happen so it is important the back four and the goalkeeper concentrate.
"I thought we did that, we are pleased we've had five clean sheets on the spin, so that is going very well."
England remain top of Group E following the win in Tallinn.