Carlisle caretaker boss Greg Abbott pointed to a "non-League" approach that put an end to Conference side Grays' FA Cup dream.
Danny Graham and Graham Kavanagh netted for the Cumbrians while Marc Bridge-Wilkinson had a goal ruled out after missing his initial penalty, and Abbott insists his side's more physical approach put the Blue Square Premier strugglers to the sword.
"It was the performance we wanted," said Abbott. "We prepared for this game slightly differently to that of a league game."
He added: "We prepared almost in a non-League way - we knew we would have to scrap for every ball and fight like non-League teams do.
"Once we did that, we got the chance the play League One football. In the end we got the result and we are through to the next round of the cup which is the be-all and end-all."
Grays boss Wayne Burnett had no complaints at the result.
"We are very disappointed," he said. "We had a number of golden opportunities which we didn't take.
"We certainly didn't look out of our depth, we competed well and for the first half I thought we were the better side.
"In the second half we were chasing the ball a bit more and it came down to who could take the chances.
"They showed in their finishing why they are a League One side."
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