Hibs set up a Europa Conference League qualifying first leg clash with Croatian side Rijeka next week after beating Santa Coloma in Andorra on Thursday to progress 5-1 on aggregate.
They open their cinch Premiership campaign against Motherwell at Fir Park on Sunday and Ross knows they will have to improve on their 2-1 midweek win.
"We face a step up over the next couple of weeks, in the league games as well," he said.
"Motherwell will provide a sterner test and everything is geared up for that game on Sunday. After that it becomes about Europe again.
"That's a new experience for us, a quick turnaround in games and having to produce a good performance, then another good performance and another good performance. We are going to have to do that. The players are excited about it.
"The players are honest enough to know they will have to bring all-round better aspects of their game to win on Sunday. But we are more than capable of doing that.
"Good players are physically strong enough to deal with that challenge, it's just making sure, mindset-wise, they maintain that strength."