Leinster made it to the semi-finals of the Champions Cup last season before losing to French outfit Clermont 27-22 at the Matmut Stadium de Gerland.
The three-time Champions Cup winners have been drawn in a pool with Montpellier, Exeter Chiefs and Glasgow Warriors this season and they kick off their campaign on home soil against the French club on Saturday.
Cullen insists he is relishing the opportunity of getting back into knockout rugby and insists the club have ambitions to be dominant in Europe once again.
"We want to get back to the stage where we're the best team in Europe,” Cullen told Leinster Rugby.
"It's proper cup knockout rugby as well. You know the pools, there's not much margin for error so it means that every game is full on.
"We would like to think we have the potential and the ability to challenge some of the best teams out there, and that's where we want to be."