Parker admitted it had been 'strange' to play at Stoke for their 1-1 draw without boss Grant.
The manager respected the Jewish holy day of Yom Kippur and stayed away in order to fast in private.
Parker said: "All week it was about whether Avram was going to be here, and I suppose it is a little bit strange when your manager is not here. But we were all professional enough to understand the reasoning and the circumstances.
"We just had to get on with it. Everyone involved did a great job. The manager has been around all week so we came here well organised - we knew what we had to do and we all put the plan into action."
Asked if Grant might now be tempted to stay away more often, stand-in boss Paul Groves laughed and replied: "You'll have to ask him!"