Despite being a heavy favorite heading into Saturday's road game at struggling Wake Forest, Bowden and the Seminoles have worked their way back into the national title picture.
Grobe knows Wake Forest could be in for problems if not prepared.
"Right now, they are a team that is hitting on all cylinders and playing really well," Grobe said.
"I know that (Virginia) is a really solid team and Florida State didn't have any problems with them.
"You can't go to sleep in one quarter. Against a team like Florida State, you have to play at a higher level for all four quarters. You need to play above your head if you want to win."
The Seminoles should see plenty of running back Chris Barclay, who has amassed 520 yards and four touchdowns.
FSU offensive coordinator Jeff Bowden was pleased with the Seminoles' preparation this week.
"I thought they practiced well this week," Bowden said.
"I saw nothing that would make me think that they weren't preparing for this game. I didn't see a lack of concentration or a bunch of missed assignments. I saw missed assignments but that's what you practice for. I thought they worked pretty good."