Arcora sat outside the leader and Allen was given the instructions of not going too early on the colt.
"It was about as close as we wanted him to be, but two-year-olds stepping up to that trip there was never going to be any tempo," Griggs said.
"Knowing the horse, you can't lead on him as he floats, and I think he had more to give there, and he was holding them well enough on the line."
Griggs said how Arcora made his way to the Derby would be left to Busuttin and Young.
"Trent and Natalie are good at getting middle distance three-year-olds up to that trip and he will follow that familiar path," Griggs said.
"There's lots of nice 2000-metre races coming up in September and October, the UCI (at Flemington), the Caulfield lead-ups, but we'll just plot a course that suits him best.
"We'll get him here on Derby Day and he'll make his presence felt."