The English side scored five tries at Murrayfield to ensure that they started their campaign with a bonus point.
"In the Heineken Cup a win is vital in the opening game but to get the extra point from scoring those tries was a real bonus," McCall told Sky Sports News.
"Edinburgh are a difficult team to play against. It was a huge credit to our boys that Edinburgh were shut out in the game."
Sarries continue their European duties with a trip to Paris to face Racing Metro on Saturday.